Colloidal Aggregates of Pd Nanoparticles Supported by Larch

Article pubs.acs.org/JPCB

Colloidal Aggregates of Pd Nanoparticles Supported by Larch Arabinogalactan Ekaterina R. Gasilova,*,† Galina N. Matveeva,† Galina P. Aleksandrova,‡ Boris G. Sukhov,‡ and Boris A. Trofimov‡ †

Institute of Macromolecular Compounds, Russian Academy of Sciences, Bolshoy Prospekt, 31, 199004 St.-Petersburg, Russia A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Division, Russian Academy of Sciences, Favorsky Street, 1, 664033 Irkutsk, Russia

‡

ABSTRACT: Palladium nanoparticles (PdNPs) are used in catalysis, hydrogen storage, biomedicine, and so on. Arranging the self-assembly of PdNPs within colloidal aggregates is desirable for improving their consumer properties. Stable widely dispersed colloidal aggregates of larch arabinogalactan (LARB) containing nanosized (5-nm) PdNPs were obtained by reducing Pd ions in alkaline solutions of LARB. Centrifugation resulted in a set of LARB−PdNP colloids ranging from 60 to 240 nm. The colloids were studied by static light scattering (SLS) and dynamic light scattering (DLS). The SLS data presented as Kratki plots correspond to a particle scattering factor of linear rather than branched chains. The fractal dimension of the LARB−PdNP colloids was found by SLS to be d = 1.96, which is between the values for diffusion- and reactionlimited aggregation. This result is ascribed to the aggregate’s internal motion, which is evident from the power-law exponent of the dependence of the DLS relaxation rate on the scattering vector, ⟨Γ⟩ ∼ qα with α = 2.24. The structure-sensitive ratio of the radius of gyration to the hydrodynamic radius was found to vary within the interval of 0.8 ≤ Rg/Rh ≤ 1.2 corresponding, to the spherical form of LARB−PdNP colloids. A spiderweblike PdNP distribution pattern was observed by transmission electron microscopy. Insertion of PdNPs did not affect the fractal dimension, the power-law exponent α, or the architecture of the pristine LARB aggregates in water. The red shift of the surface plasmon extinction observed with increasing LARB−PdNP colloidal size indicates the collective optical response of the PdNP ensemble in the colloid.

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nm).26−30 The current work is focused on the study of the structure of these LARB−PdNP colloidal aggregates. Among the methods used to study NPs, optical extinction is widely used, because the surface plasmon resonance (SPR) depends on the NP form, shape, size, and aggregation.31,32 Dynamic light scattering (DLS) is a powerful tool for the characterization of the hydrodynamic radius (Rh) of NP colloids.33 Light scattering intensity is especially sensitive to NP aggregation because of the nanoantenna effect caused by the dramatic enhancement of electromagnetic field between neighboring NPs. (The nanoantenna effect permits the detection of even a single molecule trapped between gold or silver NPs through surface-enhanced Raman scattering.34) The spherical form of LARB−PdNP aggregates facilitates light scattering analysis, whereas their wide dispersion complicates this characterization. Therefore, we fractionated LARB−PdNP colloids by centrifugation. In the current work, we used both DLS and static light scattering (SLS) for the characterization of the colloidal PdNP aggregates. In particular, the form and mass distribution within the colloidal aggregates were analyzed by

INTRODUCTION Modern interest in new hybrid materials combining metal nanoparticles (NPs) with water-soluble polysaccharides is dictated by the perspective of applying them in different areas, such as catalysis, diagnostics, and biomedicine.1−3 Polysaccharides act as both the capping agents and the nanoreactors, reducing metal ions to a zerovalent state.4−7 Palladium NPs, known to be excellent catalysts,8−11 are used in heterogeneous catalysis,12 photocatalysis and photochemistry,13−15 and for solar energy conversion and hydrogen storage.16−19 Water-soluble palladium nanoparticle (PdNP) catalysts are especially interesting for biomedical applications.20,21 Controlled organization of metal NPs is desirable for their applications.22−25 In particular, the morphology pattern of PdNP aggregates within colloids is critical for palladium-based catalysis. Because polysaccharides themselves form aggregates in water, polysaccharides present an example of capping agents promoting the formation of colloidal NP aggregates. Such colloidal aggregates are important for the use of PdNPs directly in water solutions. Recently, nanocomposites of larch arabinogalactan (LARB) and PdNPs have been shown to form spherical aggregates with sizes larger than those of a single PdNP (5 nm) and individual macromolecules of LARB (7 © 2013 American Chemical Society

Received: December 1, 2012 Revised: January 27, 2013 Published: January 29, 2013 2134

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from the upper half of the 2 mL Eppendorf tubes. Aqueous solutions of pristine LARB were not filtered or centrifuged. Light Scattering. DLS and SLS were carried out simultaneously with a goniometer equipped with a 288-channel correlator (Photocor-FC), described previously in ref 27. At each concentration, the radius of gyration Rg, was determined from the dependence of the form factor (P) on the scattering wavevector q = 4πn sin(θ/2)/λ

comparing the structure-sensitive ratio of the radius of gyration (Rg) to the hydrodynamic radius, ρ = Rg/Rh, with the values calculated for a number of models.35,36 Rg/Rh is also called the Burchard ratio. As the PdNPs are embedded in the polysaccharide matrix, it is interesting to determine whether the NPs perturb the structure and mobility of the pristine LARB aggregates. In particular, on the basis of light scattering analysis, it is possible to determine the fractal dimensions of the aggregates,37,38 to clarify the influence of the internal mobility within the aggregates on the relaxation monitored by DLS,39 and to quantify the degree of branching according to refs 40 and 41.

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P=

1 1 + (qR g)2 /3

(1)

where P = Rθ/Rθ=0, Rθ is the Rayleigh ratio, and Rθ=0 is the result of extrapolation of Rθ to θ → 0. Equation 1 was derived by Zimm for polydisperse coils in a theta solvent.43 The correlation function of the electrical field of the light scattered from the LARB−PdNP colloids, g1, was analyzed by the cumulants method44,45

EXPERIMENTAL SECTION

Synthesis. The virgin LARB was extracted from ground larch Larix sibirica in hot distilled water under stirring for 2 h at 90 °C. The extract was purified from phenol compounds by passing it through a chromatographic column filled with granulated poly(amide). The water solutions of LARB were partly evaporated at 90 °C, and then LARB was precipitated with ethanol. Unfiltered solutions contained two fractions of LARB, attributed to individual LARB macromolecules and their aggregates.27 By proper filtration, in a previous work, we removed the LARB aggregates from the water solution and characterized the individual macromolecules of LARB by SLS and DLS (Mw = 48000 g/mol, Rh = 3.7 nm).42 In the nanocomposite synthesis, PdCl2 was used as the precursor for PdNPs. The reaction was carried out at pH 11. Constant pH during the reaction was maintained by the addition of 30% sodium hydroxide. The PdNP content was 4.1% (w/w). According to X-ray diffraction analysis, the PdNP diameter was 5 nm.28 Centrifugation. Centrifugation was carried out by a laboratory centrifuge (Elmi CM-50). The nanocomposite concentration in the initial colloidal solution, c0, was varied in the range 0.3 ≤ c0 ≤ 1.2 g/L. The set of colloids was obtained by several successive centrifugations at angular speeds of 2000 ≤ ω ≤ 16000 rpm and centrifuge exposure times of 2 ≤ T ≤ 14 min. Dark precipitate appeared at the bottom of the Eppendorf tubes after centrifugation (see Figure 1). Several drops of this dark sediment solution were redispersed in 3−4 mL of distilled water. One milliliter of the supernatant colloid was collected

ln g1(t ) = −⟨Γ⟩τ + μ2 τ 2/2! − μ3 τ 3/3! + ...

(2)

where ⟨Γ⟩ is the first cumulant and μn is the nth cumulant, given by μn = ∫ G(Γ)(Γ − ⟨Γ⟩)n dΓ, where G(Γ) is the relaxation rate distribution. The distribution width is determined by Rh(PDI)1/2, where PDI = μ2/⟨Γ⟩2 is the polydispersity index. The apparent diffusion coefficient, Dapp, was determined at each concentration as Dapp = ⟨Γ⟩/q2

(3)

Assuming that the scatterers are spherical, the apparent hydrodynamic radius, Rapp h , can be calculated by the Stokes− Einstein relation, Rhapp = kBT/6πDappη, where kB is the Boltzmann constant, T is the temperature, and η is the solvent viscosity. The actual values of the hydrodynamic radius and the radius of gyration were determined by extrapolation to infinite app dilution: Rh = Rapp h (c → 0), Rg = Rg (c → 0). We found that the two radii did not depend on concentration. We ensured that the centrifuge tubes and pipettes were dustfree by rinsing them with benzene, subjecting them to a vacuum, and filling them with dust-free air. The solvent (water) was made dust-free by filtration through a syringe polyamide filter with a 100-nm-pore-size membrane (Cameo). For complete equilibration, the solutions were prepared at least 10 h before the measurements. Transmission electron microscopy (TEM) was performed on a Tecnai F30 S-TWIN TEM instrument at 300 kV with a fieldemission gun. Dry composite was ground in an agate pounder, mixed with ethanol under ultrasound treatment, and pulverized with an ultrasonic pulverizer on a copper net covered by Formvar.

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RESULTS Transmission electron microscopy (Figure 2a) revealed dark PdNPs on a background of light gray spheres corresponding to the LARB−PdNP aggregates, marked by dotted circles. The dark spiderweblike PdNP aggregates are presented at higher resolution in Figure 2b (dotted white lines are guides to the eye). The mean diameter of a single PdNP determined from Figure 2b was 6.5 ± 0.5 nm. This value is in accord with the diameter of 5 nm determined by X-ray diffraction in ref 28. Among the variety of self-assembly patterns of PdNP aggregates,46−49 wormlike and spiderweblike aggregates have

Figure 1. Photographs of LARB−PdNP colloid (c0 = 0.6 g/L) (1) before and (2) after centrifugation. 2135

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Figure 2. Transmission electron microscopy images of LARB−PdNP composite. Scale bar: (a) 50 and (b) 20 nm. The dashed lines in panel a show the spherical aggregate’s edge; the dotted white lines in panel b are guides to the eye of the PdNPs spiderweblike aggregation pattern.

Figure 4. First cumulant ⟨Γ⟩ versus q2 for the (1) supernatant and (2) redispersed sediment colloids centrifuged at ω2T = 90 × 107 rev2/min. Solid lines are the least-squares fits to eq 4; dashed lines show solely the translational diffusion contribution.

been observed. The current work shows that spiderweblike PdNP aggregates formed in the LARB−PdNP composites. Internal mobility within a polysaccharide aggregate usually affects the relaxation, probed by DLS. In particular, the powerlaw exponent of ⟨Γ⟩ ∼ qα increases with the experimental DLS window (qRh) in the range of 2 ≤ α ≤ 3. The lowest value, α = 2, is characteristic of pure translational diffusion (eq 2). The upper limit (α = 3) can be observed in flexible scatterers at qRh ≫ 1.50,51 The exponent α was determined from the slope of the log− log dependence of the first cumulant ⟨Γ⟩ of the scattering vector for each sample (Figure 3). These dependences were

The representative angular dependences of the inverse Rayleigh ratio, Rθ−1, are displayed in Zimm coordinates for centrifuged LARB−PdNP colloids and pristine LARB in Figure 5a. These dependences are linear; their slopes give the values of

Figure 5. (a) Zimm and (b) Holtzer dependences of (1,2) the redispersed sediment colloids centrifuged at ω2T = (1) 30 × 107 and (2) 90 × 107 rev2/min and (3) an unfiltered water solution of the pristine LARB at c = 3 g/L. Figure 3. Log−log dependences of the first cumulant ⟨Γ⟩ on the scattering vector for the supernatant (open symbols) and redispersed sediment colloids (solid symbols) centrifuged at ω2T = 90 × 107 rev2/ min.

the mean square radius of gyration, ⟨Rg2⟩. In Figure 5b, the same experimental results are plotted using Holtzer coordinates, qPθ versus qRg.52 Figure 5b exhibits a Holtzer maximum centered at qRg = 1.73. The values for the radius of gyration determined from the Zimm and Holtzer plots were equal within an accuracy of 15%. Because the centrifugal force is proportional to the product of the square of the angular speed, ω2, and the centrifugation time, T, we present the dependence of the colloidal radii on sup sed ω2T in Figure 6. At each value of ω2T, Rsed h > Rh , and Rg > sup Rg , where the superscripts indicate the sediment (sed) and supernatant (sup) colloids. This indicates fractionation as a result of the precipitation of the largest colloidal aggregates. The polydispersity indices of the sediment, PDIsed, and the supernatant, PDIsup, colloids are plotted as functions of ω2T in Figure 7. At ω2T → 0, both PDIsed and PDIsup tend to the PDI of the pristine colloid. The increase in PDIsup with ω2T probably indicates that the initial colloidal dispersion had an asymmetric profile.

linear for the whole set of centrifuged LARB−PdNP colloids and pristine LARB aggregates. For the majority of the LARB− PdNP colloids, the inequality α > 2 was observed. We shall return later to the determination of α values of the colloids. To extract information about the colloidal translational diffusion, we fitted the scattering vector dependence of ⟨Γ⟩ to the sum of the contributions of purely diffusive (∼q2) and purely internal (∼q3) modes ⟨Γ⟩ = Dq2 + bq3

(4)

The fitting results are shown by solid lines in Figure 4. The diffusive contribution is indicated by the straight dashed line. At each concentration, the apparent hydrodynamic radius, Rapp h , was calculated according to the Stokes−Einstein relation. 2136

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Figure 8. Dependence of the Burchard factor, Rg/Rh, of the sediment (solid symbols) and supernatant (open symbols) LARB−PdNP colloids on the centrifugation conditions.

Figure 6. Plot of Rg (solid symbols) and Rh (open symbols) of the supernatant and the redispersed sediment colloids as functions of the centrifugation conditions.

Extinction spectra, E(λ), of the centrifuged colloids, normalized to the extinction at 200 nm, are displayed in Figure 9. The spectra do not reveal the surface plasmon resonance

Figure 7. Dependences of the polydispersity indexes (PDIs) of the supernatant (open symbols) and redispersed sediment (solid symbols) colloids on the centrifugation conditions. Figure 9. Normalized UV/vis spectra of the redispersed sediment (solid symbols) and supernatant (open symbols) colloids for c0 = 1.2 g/L centrifuged at 10000 rpm for 5 min. Hydrodynamic colloidal radii are indicated.

Conclusions about the colloidal shape and mass distribution within the colloids can be drawn by using the Burchard ratio, ρ, calculated for a number of models.53−55 For example, spherical scatterers exhibit values ranging from ρ = 0.78 for uniform spheres to ρ = 1 for hollow spheres with an infinitesimal shell thickness (the mass of the sphere is concentrated at the surface); for hyperbranched structures, 1 < ρ < 1.3. The Burchard factor is also known to increase with polydispersity. The Burchard ratios of the sediment and supernatant colloids (ρsed and ρsup, respectively) are plotted as functions of ω2T in Figure 8. The observed interval of 0.80 < ρ < 1.22 corresponds to spherical scatterers differing in mass distribution and/or polydispersity. The spherical form of the colloids is in accord with the form of the dry aggregates, demonstrated by scanning electron microscopy27 and observed in the TEM image in Figure 2a. As ρ increases with the polydispersity, the ω2T dependence of ρ must be analyzed together with that of the PDI. In particular, the decrease of ρsed from 1.2 to 1.0 with ω2T can be ascribed to the corresponding decrease of PDIsed. For the supernatant colloids, the situation is different: ρsup decreased, whereas PDIsup increased with ω2T. This suggests that the dependence of ρsup on ω2T cannot be ascribed to that of PDIsup. Therefore, the difference between ρsup and ρsed is not due to the width of the colloidal size distribution. We shall return to this discussion later.

(SPR) of bare PdNPs, occurring at 220 nm according to the calculations of Creighton and Eadon.56 Instead, the LARB− PdNP extinction decays smoothly with wavelength. The extinction tail of larger colloidal aggregates is red-shifted with respect to that of the smaller aggregates. Given that the surface plasmon resonance, SPR, of an aggregate is red-shifted with size,57 we suppose that the smoothly decaying extinction is the result of the overlap of the SPRs of different PdNP ensembles.

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DISCUSSION The geometric properties of the aggregates can be described using fractal geometry.58 The fractal dimension d is an indication of an aggregate’s compactness. At qRg ≫ 1, d is determined from the SLS results as Rθ ∼ q−d. At lower Rg values, an empirical approximation of the particle scattering factor38 is often used −d /2 ⎡ 2(qR g)2 ⎤ ⎥ P = ⎢1 + ⎢⎣ 3d ⎥⎦

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(5)

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larger clusters, so p → 0. At 0 < p < 1, the possibility of internal reorganization within the aggregates leads to fractal dimensions of 1.75 < d < 2.1.67 The fractal dimensionality is related to the internal mobility within the aggregates. For example, destructive microwave treatment was shown to decrease both the d and α values of starch aggregates in ref 60. Thus, internal mobility within the LARB−PdNP aggregates is likely to explain their fractal dimension, intermediate between those of the DLCA and RLCA models. To determine whether the aggregates were dendritic, we analyzed the correspondence of the SLS data with the particle scattering factor derived for hyperbranched polymers39,40

The corresponding generalized log−log dependence of P on qRg for the centrifuged colloids is presented in Figure 10. The

Phb =

1 + Cu 2 /3 [1 + (C + 1)u 2 /6]2

(8)

where C is a branching parameter related to a number of branching points per weight-average polymerization degree. The branching parameter changes in the range of 0 ≤ C ≤ 1. For linear chains, C = 1, whereas for hyperbranched samples, exhibiting branching in each unit, C = 0. In Figure 11, we

Figure 10. Log−log dependences of the particle scattering factor on the qRg value of the centrifuged LARB−PdNP colloids (blue symbols) and pristine LARB aggregates (red symbols). The dashed line is the result of fitting to eq 5.

fitting to eq 5 yields d = 1.96 ± 0.03 for the whole set of studied LARB−PdNP colloids. The pristine LARB aggregates also exhibit the same fractal dimension, indicating that the “insertion” of Pd nanoparticles into LARB does not affect the compactness of the LARB aggregates. The correlation length, ξ, of the aggregates can be determined from the fractal form factor, expressed as59 Pfractal =

sin(d − 1) a tan(qξ) qξ(1 + q2ξ 2)d − (1/2)

(6)

The correlation length ξ is related to Rg as ξ2 =

2R g 2 d(d + 1)

Figure 11. Kratki plots (u2Pθ versus u = qRg). Solid symbols, centrifuged LARB−PdNP colloids; black crosses, aggregates of pristine LARB in water. The dotted line is the best fit to eq 6 at C = 1.

(7)

At d = 1.96, eqs 6 and 7 reduce to the Zimm dependence (eq 1) with ξ = 0.59Rg. This is the origin of the linear dependences observed for the LARB and LARB−PdNP aggregates even at qRg > 1. The fractal dimensions of the LARB−PdNP and pristine LARB aggregates fall in the interval of 1.93 < d < 2.5 commonly observed for other water-soluble dendritic hyperbranched polysaccharides (amylopectine and glycogen).60−62 Although the content of three-functional glycoside units of LARB (15%)63 is higher than those of amylopectin (5−6%)64 and glycogen (8%),65 the majority of the LARB branches consist of one or two monomer units.63 Nevertheless, the low intrinsic viscosity of arabinogalactan extracted from Western Larch suggests that LARB is a branched polymer containing a small number of long bottle-brush branches.66 The rather low fractal dimension of LARB in comparison with those of other branched polysaccharides indicates a higher content of long linear fragments in LARB. The fractal dimension of the LARB aggregates was lower than that of reaction-limited cluster aggregation (RLCA), dRLCA = 2.1, and higher than that of the diffusion-limited cluster aggregation (DLCA), dDLCA = 1.75. The difference between RLCA and DLCA is in the cluster’s sticking probability, p. In DLCA, each contact between the clusters leads to their selfassembly, so p = 1. In RLCA, only favorable contacts create

present the experimental results for the whole set of centrifuged colloids plotted on generalized Kratki coordinates, u2P = f(u). The best fit was obtained with C ≈ 1, indicating that the colloidal aggregates of LARB and LARB−PdNP were constructed from linear objects. In Figure 12, the log−log dependence of the reduced relaxation rate, Γ* = ⟨Γ⟩η/q3kT, on qRh is shown for the whole set of centrifuged LARB−PdNP colloids. The results for pristine LARB aggregates are also presented. At qRh < 0.6, the experimental points correspond to solid-sphere behavior. At qRh > 0.6, Γ* departs from the pure solid-sphere behavior, thus demonstrating the influence of internal motions on the relaxation. Nevertheless, the plateau of Γ* at high qR, intrinsic to flexible linear macromolecules (predicted at 0.071−0.07868 and experimentally observed at 0.05−0.0669,70), is absent. The least-squares fit of the log−log dependence of Γ*(qRh), performed at qRh > 0.6, gives Γ ∼ q 2.24. The power-law exponent α = 2.24 is lower than that for starch (2.8 ≤ α ≤ 2.89, ref 60), suggesting higher rigidity of the LARB−PdNP colloids and the pristine LARB aggregates. The Γ*(qRg) dependence is presented in Figure 13. The main features of the Γ*(qRh) dependence are preserved: At low qR, the solid-sphere behavior is observed; with increasing qR, 2138

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Figure 14. Schematic representation of the PdNP distributions in the small and large colloidal aggregates. The profile of the mass distribution within the aggregates, M(R), based on the Burchard factors, is shown.

Figure 12. Reduced relaxation rate ⟨Γ⟩η/q3kT versus qRh for the LARB−PdNP colloids (solid symbols) and pristine LARB aggregates at c = 3.3 g/L (asterisks). The red line shows the dependence calculated for a solid sphere.

Rh < 1.3). The latter model is in accord with the spiderweblike pattern of the PdNP aggregates demonstrated by TEM (Figure 2). The Burchard factor of the smallest colloid corresponds to a sphere with a uniform mass distribution. We suppose that the number of nanoparticles in small colloids is not sufficient to form a spiderweblike aggregate.

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CONCLUSIONS Reduction of Pd ions by LARB results in the formation of stable LARB−PdNP colloids. Fractionation of the widely dispersed spherical LARB−PdNP colloidal aggregates by centrifugation permits a set of colloids ranging from 60 to 240 nm in size to be obtained. Light scattering (DLS and SLS) demonstrated its efficiency in characterizing the colloidal form, size, compactness, and internal mobility and the PdNP distribution in the colloids. The dependence of the reduced relaxation rate, ⟨Γ⟩η/q3kT, on qRh shows that, at qRh < 1, the colloids behave as solid spheres, that is, ⟨Γ⟩ ∼ q2. At qRh >1, the internal mobility increases the power-law exponent: ⟨Γ⟩ ∼ q2.24. We fitted the branching parameter C of eq 6 and showed that the aggregates are composed of linear structures (C = 1). The fractal dimensionality of the LARB−PdNP colloidal aggregates (d = 1.96) was found to be higher than that of classical diffusionlimited cluster aggregation (dDLCA = 1.75), possibly because of the internal mobility within the LARB−PdNP aggregates. In the current work, we found that insertion of PdNPs does not affect either the fractal dimension or the internal mobility of the LARB aggregates. The structure-sensitive Burchard ratio falls in the range of 0.8 ≤ Rg/Rh ≤ 1.2, corresponding to spherical scatterers. Because the radius of gyration of the colloids is sensitive to the PdNP distribution within the aggregates, Rg/Rh = 1.2 for larger colloids indicates that the PdNPs are concentrated mainly near the surface, probably because of their spiderweblike self-assembly, as observed by TEM.

Figure 13. Reduced relaxation rate ⟨Γ⟩η/q3kT versus qRg for the supernatant (open symbols) and sediment (solid symbols) LARB− PdNP colloids. The red line shows the dependence calculated for a solid sphere. The largest supernatant colloid, displaying the same dependence as the sediment colloids, was collected at the lowest value of ω2T = 1.6 × 107 rad2/s.

Γ* does not reach the plateau. Nevertheless, there is an essential difference between the Γ*(qRg) and Γ*(qRh) dependences. Specifically, there are two Γ*(qRg) dependences: that of the larger colloids is shifted right with respect to that of the smaller ones. This contrasts one master curve for Γ*(qRh), based solely on the DLS results. Thus, similarly to the Burchard factor, the Γ*(qRg) dependence compares the results of DLS and SLS experiments, but in somewhat more spectacular fashion, supporting the observed differences between the Burchard factors of smaller and larger colloids. The Burchard factors of small and large LARB−PdNP colloids correspond to different mass distributions, M(R), within colloids (Figure 14). Because the density of PdNPs is higher than that of the pristine LARB, M(R) is controlled by the PdNP distribution. Moreover, Rg must be sensitive primarily to the PdNP distribution because the scattering intensity is resonantly enhanced by the plasmons of the PdNP ensemble and the scattering from LARB macromolecules is negligible (as demonstrated in Figure 3 of ref 27). The Burchard factor of the largest colloid (Rg/Rh = 1.2) corresponds to spherical scatterers with the mass concentrated at the surface: either hollow spheres with Rg/Rh = 1.0 (e.g., all PdNPs are near the surface) or hyperbranched PdNP clusters (1 < Rg/

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AUTHOR INFORMATION

Corresponding Author

*Fax: (+7) 812 328 68 69. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by interdisciplinary integrated Grants 85 and 134 from the Siberian Branch of the Russian Academy of Sciences (RAS), cooperation grant 1 from the Ural and Far 2139

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East Branches of RAS, and a Ukrainian-Russian joint research grant from the Russian Foundation for Basic Research (Grant RFBR 12-03-90433_Ukr_a). The authors are thankful to Ludmila Borovikova for conducting the UV/vis spectra measurements.

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