Size Distribution of Nanoparticles in Solution Characterized by

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Size Distribution of Nanoparticles in Solution Characterized by Combining Resonance Light Scattering Correlation Spectroscopy with Maximum Entropy Method (MEM-RLSCS) Bocheng Zhang, Heng Liu, Xiangyi Huang, Chaoqing Dong, and Jicun Ren Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b04166 • Publication Date (Web): 27 Oct 2017 Downloaded from http://pubs.acs.org on October 28, 2017

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Analytical Chemistry

Size Distribution of Nanoparticles in Solution Characterized by Combining Resonance Light Scattering Correlation Spectroscopy with Maximum Entropy Method (MEM-RLSCS) Bocheng Zhang, Heng Liu, Xiangyi Huang, Chaoqing Dong*, and Jicun Ren* School of Chemistry & Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, P. R. China. ABSTRACT: A single nanoparticle detection method is reported for characterizing the size distribution of noble metal nanoparticles in solution by combining resonance light scattering correlation spectroscopy (RLSCS) with maximum entropy method (MEM). The principle of RLSCS is based on the autocorrelation analysis on the resonance light scattering (RLS) fluctuations due to Brownian motion of single nanoparticle in a highly focused detection volume (less than 1.0 fL), which resembled to fluorescence correlation spectroscopy (FCS). However, RLS intensity of nanoparticles such as gold nanoparticles (GNPs) is proportional to the sixth power of sizes according to Mie theory, which is different from the optical properties of fluorescent molecules. Herein the present FCS theoretical model cannot be directly applied in RLSCS to characterize GNPs. In this study, we used GNPs as model sample, and firstly established RLSCS theoretical model for the size distribution of GNPs by using the maximum entropy method (MEM), which called as MEM-RLSCS. This model covers the contribution of single-particle brightness of GNPs to the MEM fitting process based on Mie theory. And then, we preformed the computer simulations of this model. The simulated results documented that the model proposed was able to well describe the diffusion behaviors and size distribution of nanoparticles. We investigated the effects of certain factors such as size difference, the relative concentration, and single-particle brightness, on the size distribution. Finally, we used the MEM-RLSCS for characterization of GNPs in solution, and the results obtained were in agreement with the size distribution of GNPs from transmission electron microscopy (TEM). This method is also suitable for characterization of other metal nanoparticles (such as silver nanoparticle) in solution and in situ study diffusion dynamics of nanoparticles in living cells.

INTRODUCTION Currently, some noble metal nanoparticle such as gold nanoparticles (GNPs) and silver nanoparticles were widely used as labeling probes and nanomaterials in bioassays, gene transferring, bio-imaging and photothermal therapy due to their unique optical and chemical properties.1-8Compared to commonly-used organic fluorescent dyes, GNPs have certain advantages such as excellent biocompatibility, ease of synthesis and surface functionalization, strong light absorption and scattering effect, high photothermal conversion rate, and photostability etc.9,10 It is very important for characterization and determination of the multi-parameters of GNPs (such as concentration, size, or size distribution etc.) in solution to in situ study the growth dynamics of GNPs and diffusion dynamics of GNPs in single living cells. So far, certain methods have been developed for the characterization of GNPs. However, few methods were directly applied for the measurement in the solution, or only part of the parameters (such as concentration, average size) of GNPs can be extracted. UV-Vis absorption or extinction spectrometry is an indirect but effective method to determine average size and concentration of GNPs, which are measured based on the concentration of gold atom, or absorbance, wavelength and molar absorption coefficient at the surface Plasmon resonance. These methods cannot provide information about the size distribution.11, 12 Inductively coupled plasma–mass spectrometry (ICPMS),13 atom absorption spectroscopy (AAS), and atom emis-

sion spectroscopy (AES)14 are frequently used to indirectly determine the concentration of GNPs, which are converted from the content of gold atom in the GNPs solution determined by these methods and average number of gold atom in each GNP particle. The direct detection methods are to measure the concentration by counting the particle number using optical detectors, including commercial Malvern NanoSight NS300 instrument,15 imaging-counting method16,17 and microflow cytometry.18,19 NanoSight NS300 allow the analysis of concentration of nanoparticles by visualizing and tracking the nanoparticles suspended in the solution with a camera. But the measurable concentration is limited in the range from 106 to 109 particles per mL and large size of nanoparticles. Xu et al. reported a single particle counting method for quantification of gold nanoparticles based on dark field light-scattering imaging and color image processing and counting technique.17 In the measurements, GNPs solution was firstly distributed and fixed on coverslips, and then were detected (or counted) by dark field light-scattering imaging. This method is used to sensitively determine GNP, but is not suitable for the direct detection in solution. Meanwhile, it cannot be applied for the characterization on size and size distribution of GNPs due to optical diffraction limit. The micro-flow cytometry reported by Yan et al. can provide the information on the size distribution and concentration of nanoparticles in the solution.18,19 This method shows high sensitivity and a wide linearity range, and was successfully used for the measurement of GNP concentration and size characterization. Wo et al. proposed single

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Figure 1.Schematic diagram of RLSCS method to measure the size distribution of nanoparticles in solution. (A)The free diffusion of nanoparticles in the confocal volume of FCS optical system contributes to the fluctuation of scattering light. (B)The RLSCS curves are obtained by auto-correlating the measured scattering fluctuation with decay time by RLSCS instrument. (C)The size or size distribution of nanoparticles was extracted from RLSCS curves with MEM-RLSCS method combining MEM fitting analysis with RLSCS diffusion model. Scale bar in the TEM figures is 100 nm.

nanoparticle counting method based on surface Plasmon resonance microscopy (SPRM). It can determine the absolute molar concentration of nanoparticles with unknown sizes and shapes by studying the random collisions of freely-moving nanoparticles onto a solid substrate.20 Resonance light scattering correlation spectroscopy (RLSCS) is a new single nanoparticle detection method and its principle is similar to the fluorescence correlation spectroscopy (FCS), which is widely used to study the dynamics of fluorescent proteins or its interaction in live cells.21-23 Different from the fluorescence fluctuations detected in FCS,25-28 RLSCS signal is from the resonance light scattering fluctuations due to Brownian motion of single nanoparticle in a small highly focused detection volume (less than 1.0 fL). By the autocorrelation analysis on the obtained RLS fluctuation signal, RLSCS can provide certain information on the nanoparticles in solution, such as the translational and rotational diffusion coefficients and the shape of nanoparticles.29-30It has been become another important tool to determine the hydrodynamic size of nanoparticles based on the measured diffusion time, besides dynamic light scattering method (DLS). Furthermore, RLSCS have the potential advantage over DLS in the concentration measurement. Similar to FCS technique, using RLSCS the nanoparticle concentration can be directly measured based on the obtained nanoparticle number in the detection volume fitted from their autocorrelation curves, and the detection volume value fitted from autocorrelation curves of standard organic dyes with known diffusion coefficiets.32 On comparison, the concentration measurement is difficultly achieved by DLS because it is not sensitive to the concentration change based on its working principle. However, although the correlation spectroscopy have been developed to determine the average size29,30,33 and total concentration of scattering nanoparticle,32 no report was found about the application in measuring the size distribution and relative concentrations of scattering nanoparticle. The main reason is lack of theoretical model that can well describe the diffusion behaviors of noble metal nanoparticle with some special intrinsic characteristic, such as size polydispersity via wet chemical synthesis and single particle scattering intensity highly depended on the sizes. In this paper, our motivation is to develop the RLSCS method for characterizing the size distribution of GNPs in solution by introducing Mie scattering theory and combining RLSCS with maximum entropy method (MEM-RLSCS)(Figure 1).34 Maiti

et al. has firstly applied MEM to FCS and developed MEMFCS method.35 MEMFCS has been successfully applied to study the diffusion of polymer chains, Alzheimer’s disease, and drug-induced apoptosis etc.36-39 In the theoretical part of our work, the theoretical diffusion model of RLSCS was proposed by introducing Mie scattering theory. This model is derived from FCS, but its key part has been revised due to some intrinsic characteristic of noble metal nanoparticle. According to Mie theory, light scattering intensity of nanoparticles is proportional to the sixth power of the sizes,40 which is remarkably different to the optical properties of fluorescent molecules. Meanwhile, based on the theoretical model of RLSCS, MEM-RLSCS fitting process was developed to disclose the whole dynamics information of scattering nanoparticle in the solution, and it covers the different contribution of the single-particles brightness of different sizes GNPs to RLSCS curves. In the simulation part, the effects of size difference, single-particle brightness, and relative concentration on the characterization of size distribution was investigated using the Monte-Carlo simulation41,42 and adopting the mixture system composed of two-component nanoparticles as model. This result is in line with the theoretical analysis. In the experimental part, the optimized MEM-RLSCS method was used to determine the size distribution of different sizes GNPs solution. The results of MEM-RLSCS were in good agreement with the size distribution of the GNPs obtained by TEM. THEORETICAL PART Modeling diffusion of nanoparticles in RLSCS. The principle of RLSCS was based on the autocorrelation analysis on the measured RLS fluctuations due to Brownian motion of single nanoparticle (such as GNPs) in a highly-focused detection volume. If scattering nanoparticles in the solution have the same hydrodynamics diameter and the same resonance light scattering intensity, the translational diffusion model of fluorescent molecules in FCS (eq. 1) can be adopted in the diffusion model of GNPs in RLSCS.43 1

 2   1 1 1  G D (τ ) = ⋅ ⋅ τ τ 4 D 4 D   N 1+ 2 1+ 2  ω xy  ωz 

(1) Where N is the average number of particles in the detection volume and D is the diffusion coefficient of nanoparticles.


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Here ωxy and ωz are the radii of the laser focus in the x, ydirection and z direction, respectively, at the e-2 point of the Gaussian laser beam intensity. When the nanoparticles solution for measurement is a multicomponent system composed of different sizes nanoparticles with the same RLS intensity, the translational diffusion model of the mixture system can be described with eq. 2, Ni

n

G (τ ) = ∑ i

(∑ N ) n

2

⋅

i

i=1

1  τ 1 +  τD i 

1 ⋅ 1  2 2    ωxy  τ   1 +   ⋅    ω τ    z  Di 

αi =

(2) Where Ni is the average number of nanoparticle component i in the detection volume, and τDi is the characteristic diffusion times of nanoparticle component i, which is proportional to the diameter of nanoparticle according to the Stokes-Einstein equation (eq. 3) and eq. 4. D=

kT 3πηd (3)

ωxy2 4D (4) Herein, the average size or its distribution of nanoparticle can be measured according to eq. 5 based on the obtained average diffusion time or its distribution of nanoparticle. 4kT τ D d= 3πηω2xy (5) In fact, the RLS intensity of nanoparticles is dramatically dependent on the size of nanoparticles. In a multi-component system, nanoparticles with different size show different RLS intensity. In this case, RLS fluctuation signal for generating RLSCS curves is influenced both by the brightness per GNPs Qi and their relative concentration Ni. So the contribution from the relative concentration and brightness of different size GNPs should be further considered in the correlation function. And the correlation function should be revised as follows. τD =

Qi 2 Ni

n

G (τ ) = ∑ i

(∑Q N ) n

i

i =1

αi =

(

2 i

Q Ni n

∑ Qi Ni

i =1

2

i

)

⋅

1  τ 1 +  τD i 

1 ⋅  2    ωxy  τ  1 +  ⋅    ω τ   z  Di

1

2   

(6)

Q=

଼௥ మ ఒర

ቀ

τ Di12 Ni

( ∑τ N ) n

i =1

௠మ ାଶ

ଶ

ቁ ሺ1 + ܿ‫ߠ ݏ݋‬ሻ (8) ଶ

ωxy τ −1 τ ) ⋅ (1 + ( )2 ⋅ ) −1/ 2 dτ D τD ωz τD

(10) In this MEM-RLSCS model, the diffusion time τD is considered to be a variable and α(τD) is the amplitude associated with τD. The distribution of diffusion times (α (τD) vs. τD) is obtained by an optimal fitting based on the maximum entropy method by minimizing χ2 as well as maximizing entropy S when the diffusion times of the different components are involved in a given focal volume. χ2 is defined as

1 M 2 ∑ ri M i =1

ri =

(11)

G (τ i ) − G (τ i ) c

e

σi

(12)

In eq. 11, M is the number of FCS data points. σi is the inverse of weight for the ith data. Gc(τi)-Ge(τi) is the differenced value of calculated value using eq. 6 and the experimental value. For a good fitting, χ2 is approximately equal to unity when M is sufficiently large. S is defined as n

Max S = −∑ pi ln pi i =1

pi =

Where Q is the brightness of nanoparticles, d is the diameter of nanoparticle, m is a ratio of refractive indices of the particle to the medium, Q0 is the intensity of incident monochromatic

2

i

G (τ ) = ∫ α (τ D ) ⋅ (1 +

2

௠మ ିଵ

6 Di

(9) So, αi is the distribution of the characteristic diffusion time associated with τDi. The αi is associated with the concentration and the brightness of the component i, and its physical meaning is different from that of Ni in eq. 2. Herein, if MEMRLSCS software (similar to MEMFCS software35) can fit the RLSCS curves of GNPs well, the extracted average diffusion time or its distribution can be used to distinguish the size distribution of GNPs in the solution (eq. 5). Meanwhile, the relative concentration of different size GNPs can also be measured from their average number (Ni) in the detection volume (V0).32 MEM analysis on RLSCS data. According to the MEMFCS model developed by Maiti et al., 35 a multi-component model using the maximum entropy method called MEM-RLSCS was used to study the diffusion dynamics of GNPs and extract their size distribution in the solution. G (τ) in eq. 6 can be rewritten to obtain a continuous distribution of diffusion time using MEM-RLSCS as

χ2 =

(7) Where αi is the relative weight of the nanoparticle component(i). This weight is not simply proportional to the relative concentration Ni of the individual species, but is also related to their brightness Qi (deﬁned as the number of photons recorded per particle per unit time). Eq. 6 shows the contribution from the number and brightness of different sizes GNPs to the correlation function. According to Mie theory (eq. 8), the brightness of GNPs is proportional to the sixth power of the sizes when their sizes are much smaller than the wavelength of light.40 గర ௗ ల ொబ

light, θ is the scattering angle, r is the distance between the particle and the detector, and λ is the wavelength of illuminated light. Meanwhile, according to eq. 5 the sizes of nanoparticle are proportional to the characteristic diffusion time. So the brightness of the nanoparticles is proportional to the sixth power of the characteristic diffusion time τDi. After taking the relative concentration and brightness into account, eq. 7 should transferred to eq. 9 as following,

12 τ Di Ni n

∑τ Di Ni 12

i =1 n

s.t.∑ pi = 1 i =1


(13)


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In MEM-RLSCS fitting process, the influence of brightness has been taken into account as the definition on the S and Pi. METHOD AND EXPERIMENTS The simulation. The simulation programs were written with Matlab software (MathWorks, Inc.) and executed on a personal computer. The simulation parameters were set to be close to the counterparts employed in the real experiments described later.42 The similar parameters setting and simulation procedure can be found in our previous work.22 RLSCS Instrument. The RLSCS was performed on a RLSCS instrument similar to FCS system.30 Briefly, an inverted microscope (IX71, Olympus, Japan) was applied as the optical stage. A He-Ne laser beam with 632.8 nm wavelength (Hongyang Laser Co., Shanghai, China) was expanded with a telescope, and then focused into a sample solution by water immersion objective (UplanApo, 60×/N.A. 1.20, Olympus, Japan). The sample with about 20 µL was placed on a coverslip with thickness of about 170 µm (#1, Fisher, U.S.A.). The scattering light from the sample was collected by the same objective and passed through a dichroic mirror (640DRLP, Omega optical, U.S.A.), and then was focused into a pinhole (35 µm) on a single photon counting module (SPCM-AQR16, Perkin-Elmer EG&G, Canada). The yield signal was tracked and correlated by a multiple-tau autocorrelator card (Flex0212D, Correlator.com, U.S.A.). In the RLSCS system, no emission filter is used different from FCS system. All data were analyzed with eq. 6 for nanoparticles diffusing in a threedimensional Gaussian volume element and nonlinearly fitted with the Origin 6.1 software package based on the LevenbergMarquardt algorithm. Preparation and characterization of GNPs. The GNPs were prepared according to the method in the reference.45 In brief, aqueous solution of HAuCl4 (0.01%, w/w) and sodium citrate (1%, w/w) were prepared. Ultra-pure water (Millipore Co., USA) was used in all experiments. The 0.01% HAuCl4 (100 mL) solution was heated to boiling, and then 1% sodium citrate solution (the added volume will determine the size of GNPs) was added rapidly to the boiling solution. Heating continued for 30 minutes after the solution color kept stable. After cooling to room temperature, the GNPs solution was stored in 4 oC for further applications. The sizes of four GNPs were characterized by TEM (JEOL-2100F, Japan). RESULTS AND DISCUSSION The simulation. As reported in our previous work, MonteCarlo simulation was used to simulate the diffusion motion of metal nanoparticles in the solution (Fig. S1 and S2).22 The parameters including concentration, single particle brightness, diffusion coefficient or characteristic diffusion time of nanoparticles, were initially set to simulate diffusion dynamics. Then, RLSCS curves (G (τ)) were obtained from the autocorrelation analysis on the fluctuation of resonance light scattering produced by the random motion of nanoparticle. Finally, MEM-RLSCS fitting program was used to fit these synthetic G (τ) curves with the theoretical model and figured out these parameters. Consequently, if the theoretical model and MEMRLSCS fitting program are effective, the fitted parameters will be in accordance with their initially set value. With that, the difference between the set value and the fitted value of a certain parameter can be regarded as an indicator of the reliability and adaptability of the model. One-component simulation was, firstly, conducted for single

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Figure 2.The simulated RLSCS curves (A) and their fitting curves of single component nanoparticles with the diffusion model. (B-E) Their diffusion time distribution curves resolved with MEM-RLSCS method. Their different coefficients were set as 600 µm2/s (B), 300 µm2/s (C), 120 µm2/s (D), and 60 µm2/s (E), respectively. Table 1.The diffusion coefficients of simulated nanoparticles by MEM-RLSCS method The set (µm2/s)

MEM-RLSCS (µm2/s)

RSD (%)

600 300 120 60

550 276 109 54

5.73 5.79 10.4 12.5

component nanoparticle systems, in which the nanoparticle concentrations are same but their diffusion times or corresponding sizes vary. The effect of nanoparticle concentration on the simulation and the accuracy of the simulation program are shown in the Supporting Information (Fig. S3 and Table S1). Four virtual samples with different diffusion coefficients set were simulated by Monte-Carlo program and fitted with MEM-RLSCS method. Fig. 2A is the simulated RLSCS (circle) and fitted (colored solid line) curves of different sizes particles. It is observed that the RLSCS curves shift right with the set diffusion coefficient decrease (or sizes increase). Meanwhile, MEM-RLSCS program was used to fit the RLSCS curves. The fitted curves can well overlap with the raw RLSCS curves, which can ensure that the contribution of all particles to diffusion dynamics have been included in the extracted diffusion time distribution curves by MEM-RLSCS method.35 the diffusion time distribution of each virtual sample is shown in Figure 2B-E. And the measured average diffusion coefficient and its distribution were nearly same as set in the simulation program, as shown in Table 1. The differences between the diffusion coefficients set by system with average diffusion coefficients determined by MEM-RLSCS were less than 10%, and the relative standard deviations (RSD) from 20 simulations were between 5% and 13%. MEM was a tool that searched the most stable diffusion time or size distribution of nanoparticles. Two-component simulation was, secondly, conducted to verify the feasibility of the method to discriminate the size distribution. Two-component systems were set by varying their relative diffusion times of components but with the same concentration and brightness. The ratios of diffusion time of two components were set as 1.5:1, 2:1, and 5:1 to indicate their size difference, respectively. The diffusion time distribution curves are shown in the Fig. S5. When the ratio of diffusion times is more than 2:1, two components appear with two


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Table 2.The brightness influence on the relative concentration measurement and its calibration

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Brightness ratio

The set relative concentration ratio

Without brightness calibration

With brightness calibration

4:1 3:1 2:1 1:1 1:2 1:3 1:4

50% : 50% 50% : 50% 50% : 50% 50% : 50% 50% : 50% 50% : 50% 50% : 50%

100%:0% 91.2%:8.8% 79.8%:20.2% 44.9%:55.1% 22.8%:77.2% 15.7%:84.3% 0%:100%

N.A. 54.4% : 45.6% 49.5% : 50.5% 46.2% : 54.8% 48.6% : 51.4% 55.3% : 44.7% N.A.

Abbreviation: N.A.: not applicable. separate peaks in the curves. And the diffusion time values in the peak positions are in accordance with the set in the program. When the ratio is less than 1.5:1, the MEM-RLSCS method cannot distinguish the difference between two components. And the broadened distribution compared with that of single component showed that it was the mixture of two components. The result suggests that, MEM-RLSCS method have the capacity to distinguish the size or its distribution of different components from the mixture when the size difference is more than the ratio of 2:1.

Figure 3.The diffusion time distribution of simulated two component mixtures with same brightness but with different concentration ratio (A- 9:1; B-8:2; C-7:3; D-6:4; E-5:5; F-4:6; G-3:7; H-2:8; I-1:9). Next, two-component simulation was conducted to verify the capability that extracts their relative concentration information from the mixture. Two-component systems were set by varying their relative concentration but other parameters remained consistent. The ratio of diffusion times of two components was fixed as 5:1. And their concentration ratio varied from 9:1 to 1:9. The RLSCS curves and the size distribution results are showed in the Fig. 3 and Table S2. Fig. 3 demonstrates that when the percentage of one component is less than 10%, the component cannot be distinguished by MEM-RLSCS method. And the peak positions of two components do not change with their relative concentration. It suggests that the relative concentration do not influence the MEM-RLSCS method to figure out the size or distribution. Meanwhile, the concentration ratio obtained by MEM-RLSCS was much close to that set by system as shown in Table S2. The above results suggest that, MEM-RLSCS is reliable and accurate in the characterization on the size distribution and concentration distribution.

Finally, simulations were performed to investigate the influence of scattering light brightness on MEM-RLSCS analysis. As shown in Table 2, their brightness ratio between two components varies but their concentrations are same. The relative ratio of diffusion time was fixed as 5:1. As showed in the Fig. S6 and Table 2, although the constant peak positions showed that the brightness did not influence the measurements on their size, it can remarkably influence the accurate measurement on relative concentration. The concentration discrepancy increases with the increase of brightness ratio. It indicates that the proper calibration to eliminate the influence of brightness difference on the concentration measurement is required. After the calibration was performed according to the proposed MEM-RLSCS theoretical model with eq. 13, the measurement results can be much close to the set values (Table 2). The above Monte-Carlo simulation on MEM-RLSCS analysis suggests that, the MEM-RLSCS theoretical model was successfully established by combining RLSCS with MEM, and this model can cover the contribution of the brightness of GNPs to MEM fitting process due to the introduction of Mie scattering theory. By MEM-RLSCS fitting on the simulated SNPs samples, the size distribution and relative concentration of simulated samples is in line with the theoretical analysis. Characterization on the size distribution of GNPs. To examine the accuracy and reliability of MEM-RLSCS in the size characterization on real samples, GNPs solutions with sizes of 20 nm, 40 nm and 60 nm from BBI Inc. were analyzed (Figure 4). These curves show that, the characteristic diffusion time increased with size increase of GNPs. Table 3 shows the results measured by TEM and MEM-RLSCS. The determined average diameters of GNPs by MEM-RLSCS are slightly larger than that by TEM. And the size distributions determined by MEM-RLSCS were in accordance with that by TEM. Meanwhile, GNPs sample prepared with the citrate-reduction method in our lab was analyzed (Figure 4B). On comparison, the results both from TEM and MEM-RLSCS show that the size distribution of sample prepared in our lab is larger than that provided by the BBI Inc. These results suggest that MEMRLSCS is an accurate tool in measuring the size and its distribution of GNPs. The existence of random aggregation of nanoparticles in the solution leads to the bigger average diameter and wider size distribution. But it seems for MEM-RLSCS to more truly reflect the real state of GNPs in the solution that can directly measure from the solution different to TEM. The smallest size for characterization with this MEMRLSCS method was verified to be about 13 nm, which is determined by the available resonance light scattering signal for RLSCS of GNPs that depend on its size, laser wavelength, and



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Figure 4. RLSCS curves of difference sizes GNPs (left column) and their diffusion time distribution curves (right column) resolved with MEM-RLSCS method (A-19.2 nm; B-30.6 nm; C-38.7 nm; D-59.1 nm). Inset is their TEM images. Scale bar is 100 nm. Table 3.The size or distribution of GNPs solutions measured The relative concentration measurements of GNPs mixby MEM-RLSCS and TEM tures. In order to verify the feasibility of MEM-RLSCS to measure the relative concentrations of different components in TEM RSDTEM MEM-RLSCS RSDMEM the mixture, the newly-prepared 19.5 nm GNPs solution was ( nm ) ( nm ) spiked with the different concentration of 42.5 nm GNPs for samples. The ratios of the relative concentrations of 42.5 nm 4.3% 20.1 7.7% 19.2 GNPs to 19.5 nm GNPs were set from 1:400 to 1:1600. It was 8.1% 31.1 17.5% 30.6 observed that, the spiked quantity of 42.5 nm GNPs greatly 5.2% 40.0 12.1% 38.7 affect the relative abundance in the diffusion time distribution 4.1% 62.0 5.9% 59.1 curves (Figure S8). Table S4 shows the relative concentration of two GNPs determined by MEM-RLSCS after the influence of brightness of GNPs is calibrated. The measurement results intensity for illumination. The upper limit of size is about oneare in accordance with the set values. This data proved that tenth of laser wavelength, which can be further extended with MEM-RLSCS achieved the concentration measurement of other equations similar to eq. (8) describing the actual relaGNPs and their mixtures with the specific ratio. tionship between the brightness and particle sizes. And the CONCLUSION further experiments on two GNPs samples (14.3 nm and 19.1 In this work, we described a single nanoparticle detection nm) with MEM-RLSCS (Figure S7 and Table S3) verified its method to characterize the size distribution of noble metal capacity to characterize different GNP with size differences nanoparticles in solution by combining resonance light scatterless than 5 nm. ing correlation spectroscopy (RLSCS) with maximum entropy


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method (MEM). We proposed a new theoretical model for diffusion of nanoparticles in RLSCS system by introducing the Mie theory into the autocorrelation functions. Based on the model, MEM-RLSCS analysis method was developed to study the diffusion dynamics of GNPs and extract their size distribution in the solution. Different to the conventional MEMFCS, MEM-RLSCS covers the contribution of single-particles brightness of nanoparticles to the fitting process. The MonteCarlo simulation results demonstrated that the model is able to well describe the diffusion behaviors of GNPs. The effects of the size difference, the relative concentration, and singleparticles brightness was simulated and investigated. The results obtained from different GNPs were in agreement with the size distribution of GNPs measured with TEM experiments. The RLSCS theoretical model and MEM-RLSCS method can be an effective and accurate tool in characterization of GNPs. Compared to current methods, MEM-RLSCS is a nondestructive, multi-parameter detection method (size, size distribution, and concentration) and shows the minimum requirement for sample volume(more than 1.0 fL), short analysis time and simple operation steps. It is also well suitable for characterization of other metal nanoparticles (such as silver nanoparticle) in solution and in situ study the diffusion dynamics of nanoparticles in living cells.

AUTHOR INFORMATION Corresponding Author *Tel: 86-21-54746001. E-mail: [email protected], [email protected].

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was financially supported by NFSC (21475087, 21327004, and 21135004), and SMC-Chenxin Young Scholar project sponsored by Shanghai Jiao Tong University.

ASSOCIATED CONTENT Supporting Information The Supporting Information (the supplemental figures and table (PDF)) is available free of charge on the ACS Publications website.

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Size Distribution of Nanoparticles in Solution Characterized by

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