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Determining the Absolute Concentration of Nanoparticles Without Calibration Factor by Visualizing the Dynamic Processes of Interfacial Adsorption Xiang Wo, Zhimin Li, Yingyan Jiang, Minghe Li, Yu-wen Su, Wei Wang, and Nongjian Tao Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.5b04386 • Publication Date (Web): 19 Jan 2016 Downloaded from http://pubs.acs.org on January 27, 2016
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Analytical Chemistry
Determining the Absolute Concentration of Nanoparticles Without Calibration Factor by Visualizing the Dynamic Processes of Interfacial Adsorption Xiang Wo†, Zhimin Li†, Yingyan Jiang†, Minghe Li†, Yu-wen Su‡, Wei Wang*†, Nongjian Tao† † State Key Laboratory of Analytical Chemistry for Life Science, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, China ‡ School of Pharmacy, Nanjing Medical University, Nanjing 211166, China ABSTRACT: Previous approaches of determining the molar concentration of nanoparticles often relied on the calibration factors extracted from standard samples, or required prior knowledge regarding the geometry, optical or chemical properties. In the present work, we proposed an absolute quantification method that determined the molar concentration of nano-objects without any calibration factor or prior knowledge. It was realized by monitoring the dynamic adsorption processes of individual nanoparticles with a high-speed surface plasmon resonance microscopy. In this case, diffusing nano-objects stochastically collided onto an adsorption interface and stayed there (“hit-n-stay” scenario), resulting in a semi-infinite diffusion system. The dynamic processes were analyzed with a theoretical model consisting of Fick’s laws of diffusion and random-walk assumption. The quantification of molar concentration was achieved on the basis of an analytical expression, which involved only physical constants and experimental parameters. By using spherical polystyrene nanoparticles as a model, the present approach provided a molar concentration with excellent accuracy.
Various kinds of bio-conjugated nanomaterials have attracted rapidly growing interest in sensing, diagnosis and nanomedicine.1-3 The number/molar concentration of nanomaterials is one of the most critical parameters to be characterized in order to achieve efficient preparation, quality control and clinical administration. For example, as polymer nanoparticles have become promising platforms in the development of smart drug-carriers4, it is necessary to determine the molar concentration of nanoparticles for the reliable bio-conjugation and for the accurate drug administration. Although seems simple, the accurate determination of the molar concentration of arbitrary nanomaterials has been a long-standing challenge, mainly because of the intrinsic heterogeneity of nanomaterials.5 The present approaches for the quantification of the nanoparticle concentration generally drop into two categories, ensemble measurement and single nanoparticle counting. In the ensemble measurement, physical or chemical properties averaged from nanoparticles ensembles, such as geometrical size and extinction coefficient, are utilized to quantify the number of nanoparticles.6 For instance, based on the amount of gold precursor existed in the flask and the average number of atoms per nanoparticle, one is able to estimate the molar concentration of gold nanoparticles. This method has been routinely adopted in laboratory to estimate the concentration of as-synthesized nanoparticles. In this case, prior knowledge on the shape and size distribution of gold nanoparticles needs to be pre-characterized to calculate how many gold atoms, in average, are contained in one nanoparticle. However, different from their molecular counterparts, nanomaterials do not have precise chemical components at atomic level. Each nanoparticle is unique in terms of size,
morphology and surface chemistry. This feature resulted in more or less inaccuracy when utilizing the average property from nanoparticle ensembles. The uncertainty on the reaction efficiency as well as the inevitable aggregation further reduced the accuracy when determining the molar concentrations. Single nanoparticle counting has been emerging in the last few decades and has proven to be powerful in chemical and bio-analysis as it measures the number of nanoparticles at single nanoparticle level.5,7 So far, many single nanoparticle counting techniques have demonstrated their capabilities to quantify the molar concentration of nanoparticles, including optical scattering,8-11 fluorescence,12 electrochemistry,13,14 and induced coupled plasma mass spectroscopy.15-17 Typically, when a single nanoparticle trespasses into a predefined detection region, it alters the optical, electrochemical or mass/charge properties, and induces a detectable signal identifying the appearance of single nanoparticles. Counting the single nanoparticle events provides the direct information regarding the number concentration of nanoparticles. Although powerful, most of these single nanoparticle counting techniques provide relative quantification, which means they often require standard samples and calibration curve to compensate the uncertain efficiencies during sample capture and signal transductions.18 Because it is usually difficult or sometimes impossible to access the standard samples of bio-conjugated nanoparticles, absolute determination of nanoparticle concentration, without the need of standard samples and precharacterized factor, is highly demanded. In the present work, we proposed an absolute determination of molar concentration of nanoparticles with unknown sizes and shapes by studying the dynamic processes of interfacial
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adsorption. This method involved the random collisions of single nanoparticles onto a solid substrate driven by Brownian motion, and a home-built surface plasmon resonance microscopy (SPRM) that can count the number of collision events during a certain period of time, i.e., the collision frequency, in a real-time manner. We subsequently established a physical model to understand the time-dependent interfacial collision frequency. In this model, the absolute concentration of nanoparticles can be analytically expressed in an equation consisted of only physical constants and experimental parameters. As a result, one can calculate the molar concentration of nanoparticles completely based on the experimental results from one set of sample running, without any prior knowledge regarding the geometry of the nanoparticles and the calibration factors from standard samples. EXPERIMENTAL SECTION Materials and characterization. Polystyrene nanoparticles were purchased from Janus New-Materials as aqueous solution and used without further purification. Appropriate amount of polystyrene nanoparticle solution was diluted by 26 times with deionized water (DIW, 18.2 MΩ·cm resistivity) and mixed with 1XPBS in the chamber on top of SPRM microscope to reach a final dilution factor. All the diluted solutions were sonicated for 5 minutes before use. The DIW produced by Barnstead Smart2Pure3 UF (Thermo Fisher) was used throughout the research. Transmission electron microscopy (TEM, JEM-2100, JEOL) and dynamic light scattering (DLS, Nano-ZS90, Malvern) were used to measure the actual size of polystyrene nanoparticles. The zeta potential of as-used polystyrene NPs was -42 mV (Nano-ZS90, Malvern). Atomic force microscope (5500, Agilent Technologies) was used to characterize the gold substrate before and after the adsorption of NPs. Electrochemical impedance spectroscopy (EIS) measurement was performed with an electrochemical workstation (PGSTAT302N, Metrohm Autolab). Surface Functionalization. The gold chips were BK-7 glass cover slips coated with 2 nm chromium and then with 47 nm gold. Each Au chip was rinsed with DI water and ethanol, and blown dry under nitrogen before use. After further cleaned by hydrogen flame to remove possible remained contaminations, the chip surface was modified with 1mM PEG in 10mM NaBH4 under the temperature of 4 ᵒC overnight. When the self-assembly of CH3O-(CH2CH2O)n-CH2CH2-SH (MW = 350, NanoCS Inc.) was finished, the chip was thoroughly rinsed with DI water prior to use. SPRM setup. The experiment of SPR imaging was performed on an inverted microscope (Olympus IX83) by using a high numerical aperture oil immersion objective 60X (NA = 1.49). A red super luminescent light emitting diode (SLED) with wavelength of 680 nm (Q-photonics, operating power 0.2 mW) was used as the light source, and a polarizer was inserted in the optical path to generate p-polarized light so as to excite the surface plasmon wave. The power density of incident light was ~6 mW/mm2. Under such a low power density, the nanoparticles were stable for hours without any heating damage. The incident angle of such light was also optimized for the purpose of delivering largest surface plasmon response from polystyrene. The SPR chip was placed on the objective with index-matching liquid. The SPRM images were recorded by a CCD camera (Pike F-032B, Allied Vision Technologies) at a
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frame rate of 13.2 fps (hitting frequency measurement) or 1067 fps (diffusion coefficient measurement). COMSOL simulation. Three-dimensional simulation of the SPRM image of single polystyrene nanoparticle was performed with COMSOL multiphysics software. The geometrical model was consisted of glass layer, gold layer and water layer (from bottom to top), respectively. The dimensions of the gold film were 5 µm × 4 µm × 47 nm. A polystyrene nanoparticle (r = 100 nm) was placed on top of the gold film and the distance between nanoparticle bottom to the gold film was adjusted from 0 to 200 nm. A p-polarized plane wave (TM wave) with an incident angle of 70.0 deg was adopted as the excitation source. The refractive indices of glass, gold, water and polystyrene were set to be 1.51391, 0.16146 + 3.6420i, 1.331, 1.60, respectively. The electrical field distributions at the gold-water interface were calculated at different nanoparticle-substrate distance. The results were shown in Figure 3b. RESULTS AND DISCUSSION Imaging single nanoparticle collision with SPRM. We first demonstrate the capability of SPRM to visualize the hit-nstay events of multiple nanoparticles simultaneously.19 SPRM is an optical microscopy that can map the distribution of refractive index with a spatial resolution close to optical diffraction limit.20 The detailed description of SPRM can be found in previous work published by us and others,20-22 while the principle is briefly introduced here (Figure 1a). Gold-coated coverslip was placed on top of an oil-immersed high numerical aperture objective. An incident light was shined onto the coverslip with a certain incident angle to excite the surface plasmon wave, which exponentially decayed along the vertical distance with a typical penetration depth of a few hundred nm. The reflected light was captured with a CCD camera to produce a SPRM image. The existence of a nanoparticle influenced the surface plasmon wave and resulted in a change in the SPRM image. By subtracting the SPRM image in the absence of nanoparticles from the one before nanoparticle stroke the gold film, one was able to obtain the SPRM image of nanoparticles. Lower panel in Figure 1a shows a typical SPRM image of ~20 individual polystyrene nanoparticles, from which the total number of nanoparticles and the location of each nanoparticle was obtained. Each nanoparticle appeared as a special pattern with parabolic waves, in which the center point identified the location of nanoparticles and the parabolic tail represented the propagating direction of surface plasmon wave.
Figure 1. (a) Schematic illustration of SPRM setup. A typical SPRM image of multiple nanoparticles is provided at the
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Analytical Chemistry
bottom panel, in which each nanoparticle appears as a white pattern with parabolic tails. (b) In the presence of an adsorption layer, individual nanoparticle diffuses onto the interface and stayed there (“hit-n-stay” scenario). The formation of the diffusion layer resulted in the decreased concentration gradient. A decreased collision frequency with time is therefore recorded (green curve). The number of nanoparticle collision events was obtained by counting the parabolic patterns in the SPRM image with a home-built background segmentation algorithm written by Matlab. Although the spatial resolution of SPRM enabled the simultaneous detection of hundreds of nanoparticles, in the present work, the number of nanoparticle collision events was controlled to be less than 20 per frame (by adjusting the frame rate and the dilution factor of nanoparticle solution) in order to avoid the significant overlapping of parabolic patterns. Such overlapping decreased the recognition accuracy of our background segmentation algorithm. It has been shown that SPRM can image not only the plasmonic nanoparticles such as silver21 and gold23, but also nonplasmonic ones such as polystyrene,22 hydrogel,24 SiO2 and virus19. SPRM signal of nanoparticles decreased as cubic power of the nanoparticle size, which made it more suitable to detect small nanoparticles. The setup we are using is able to detect gold nanoparticles as small as 10 nm,25 and SiO2 nanoparticles as small as 30 nm. Semi-infinite diffusion system. The gold film surface was chemically modified with CH3O-(CH2CH2O)n-CH2CH2-SH (PEG) molecules to ensure the strong and permanent adsorption of nanoparticles on gold film. It was believed that hydrophobic interactions and van der Waals force were responsible for the interaction between polystyrene NPs and PEG layer on the gold substrate. In this case, nanoparticles in solution stochastically stroke the gold film due to Brownian motion, and stayed on it, i.e., a “hit-n-stay” scenario. As shown in Figure 1b, the permanent adsorption of nanoparticles created a zeroconcentration interface and resulted in the formation of a diffusion layer with increasing thickness and decreasing concentration gradient. Based on Fick’s law of diffusion, one could expect the hitting frequency of nanoparticles decreased with time, as described in the classical Cottrell equation (Eq. 1):
/ / Eq. 1 / where f(t) is the hitting frequency as a function of time, NA is Avogadro’s constant, A is the area of the observation region, D and C0 are the diffusion coefficient and the molar concentration of nanoparticles, respectively. The detailed description of Eq. 1 was provided in the Supporting Information. It was clear that the presence of the adsorption interface resulted in the decreased hitting frequency of nanoparticles at a power of -0.5 with time. In order to record the hitting frequency, SPRM was employed to monitor the dynamic adsorption processes of polystyrene nanoparticles. In a series of SPRM images continuously captured at a frame rate of 13.2 frames per second (fps), the counts of parabolic-shaped patterns appeared in the differential SPRM image was considered as the hitting number during this period of time (~150 msec). Hitting frequency was calculated from the product of hitting number and frame rate. Differential SPRM images were obtained by subtracting the previous image from the present one. The nanoparticle solution =
was diluted by 676 times in order to reduce the simultaneous collision events. Figure 2a displays the experimental curves of hitting frequency (counts per second) versus time for nanoparticle solutions with different dilution factors. In all three cases, the hitting frequency was indeed found to decrease with time. This curve can be well fit with a power function as described in Eq. (1), in which the time constant was defined as α = NAAD1/2π-1/2C0, with a unit of sec-1/2. From the definition of time constant α above, the time constant was expected to be proportional to the molar concentration of nanoparticles (C0). In order to verify this point, different hitting frequency curves were recorded in three solutions with increasing dilution factors (Figure 2a). Three time constants were subsequently obtained by fitting the curves with Eq. (1). It was indeed found that the time constants linearly increased with the relative concentrations as shown in the inset of Figure 2a, indicating the validity of the diffusion model. Curve fitting using power functions was sometimes less robust than linear functions. Thus we performed a dual logarithmic transform to Eq. (1) to generate a linear expression of hitting frequency vs. time as below: log = −0.5 log + log Eq. 2
The dual logarithmic transformation was applied to the original hitting frequency curves in Figure 2a, and the results are shown in Figure 2b. Obtained curves were subsequently fitted with the linear function in Eq. (2). For all the three curves, the slope was found to be close to -0.5, and the intercept increased with the relative concentration. It is critical to ensure that the surface coverage of adsorbed nanoparticles to be low enough so that the nanoparticle adsorption was not interfered by existing ones. In a typical experiment, we counted less than 5,000 nanoparticles in total. Considering the cross section area of single nanoparticle (r = 107 nm) is ~0.036 µm2 and the area of observation region is 19200 µm2 (120 µm × 160 µm), the final coverage was smaller than 0.9%. It is believed that such a low surface coverage would induce subtle disturbance on the Brownian motion and adsorption behavior of new nanoparticles. Single particle counting enabled the analysis of nanoparticles with ultralow concentration, because rare collision events could be detected with reduced frame rate. Even if we diluted the nanoparticles by 250,000 times (final nanoparticle concentration is about 50 fM), SPRM is still able to record a hitting frequency curve that is decaying with time during a record time of 4 hours as shown in Figure 2c. This curve also matched with the diffusion model very well, with a time constant of 0.67 sec-0.5.
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Figure 2. (a) Recorded collision frequency gradually decrease with time due to the reduced concentration gradient in the diffusion layer. Semi-infinite diffusion models (solid lines) are introduced to fit the collision frequency curves (scattered dots) for nanoparticles solution with different dilution factors. Inset: The time constant (α) is proportional to the relative nanoparticle concentration. (b) Linear relationships are found in the log-log scale plots of the same collision frequency curves. The slopes are close to -0.5 as predicted by the semi-infinite diffusion model. (c) Recorded collision frequency curve for a polystyrene sample that was diluted by 250,000 times (~50 fM). The determination of diffusion coefficient D. As the time quently, SPRM signal of a single nanoparticle also exponenconstant, α, involves only two unknowns (D and C0), C0 can tially decays with the vertical distance as described in Eq. be determined if the diffusion coefficient is known. By taking (3):23 advantage of the near-field feature of surface plasmon wave, * ! = !"#$ ⋅ exp )− , Eq. 3 we successfully tracked the vertical trajectory of individual *+ nanoparticles during interfacial adsorption, from which the where Imax is the maximum SPRM signal that the nanopartidiffusion coefficient can be measured. Note that, instead of cle can achieve, z is the vertical distance between nanoparticle estimating diffusion coefficient from Stokes-Einstein equation and substrate, and zp is the distance constant. which required hydrodynamic radius of nanoparticles, we directly measured the diffusion coefficient without any Distance-dependent SPRM signal of single nanoparticles knowledge of nanoparticles geometry. has been well established in our previous work studying the oscillation of charged nanoparticles along vertical direction under alternating current electrical field.23,26 By using both experimental results and theoretical validation, the distance constant was determined to be 104 nm. This is a constant that was not influenced by the size and chemical components of nanoparticles. In order to confirm this point, we further applied a 3-D COMSOL model to determine the distance constant for polystyrene nanoparticle with different sizes. The simulated SPRM image of single polystyrene nanoparticle (left panel in Figure 3b inset) well reproduced the major features of experimental results (right panel). The SPRM signal of the same polystyrene nanoparticle was found to exponentially decay with the increased nanoparticle-substrate distance. The distance constant was determined to be 104 nm for polystyrene nanoparticles (Figure 3b), close to previous constants for gold nanoparticles.23,26 Such consistence further supported the factor that this distance constant is a function of optical system and it is independent with the chemical component and geometry of nanoparticles. A one-dimensional random-walk assumption was utilized to extract the diffusion coefficient of single nanoparticles from Figure 3. (a) Surface plamson wave exponentially decays its vertical trajectory z(t). By assuming a Brownian motion, with increasing vertical distance. The same nanoparticle exthe vertical displacement of nanoparticle can be expressed hibits larger SPRM contrast at closer distance. (b) Simulation as * = * − √2 . When we combine this relationship with of the relationship between SPRM signals and vertical disEq. (3), the quantitative expression of SPRM intensity versus tance using 3-D COMSOL model. Inset shows two SPRM time was given by: images from 3-D simulation (left) and experimental results z − √2Dt (right), respectively. (c) SPRM signal increases when a nanoI = I012 ⋅ exp )− , z6 particle approaches to the substrate, until it hits the surface. (d) z Calculated diffusion coefficients of 60 individual nanoparti= I012 ⋅ exp )− , ⋅ expβ√t Eq. 4 cles follows a Gaussian distribution. z6 As an interfacial phenomenon, surface plamson wave exponentially decays with vertical distance (Figure 3a). Conse-
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√2D √2D = z6 104nm
We recorded the continuous snapshots of a single nanoparticles collision event with a frame rate at 1067 fps. A typical SPRM signal versus time is shown in Figure 3c. It was found that the approaching of a single polystyrene nanoparticle resulted in rapidly increasing SPRM signal until it hit the substrate. Since this time point, a plateau was observed in the curve, indicating the nanoparticle stayed on the area of collision without any further movements. We subsequently fitted the recorded Ispr – t curve with Eq. (4), leading to a diffusion coefficient D of 3.0×10-12 m2/sec. Similar fitting model was applied to ~60 individual nanoparticles and the distribution of D is shown in Figure 3d. A Gaussian distribution was found with an average D of 5.1×1012 m2/sec, and the deviation was 2.2×10-12 m2/sec. As the polystyrene nanoparticles are nicely spherical with an average radius of 107 nm (independently measured by transmission electron microscopy, TEM, see supporting information), we further calculated the theoretical diffusion coefficient to be 1.9×10-12 m2/sec by using Stokes-Einstein equation. This value is about two times smaller than the number determined from single particle tracking, indicating the different diffusion dynamics in the presence of an interface compared with homogeneous solution. Note that in order to reduce the possible long-range electrostatic interactions between charged nanoparticle and charged interface, the gold film was functionalized with neutral CH3O-(CH2CH2O)n-CH2CH2-SH molecules. The determination of molar concentration C0. Once the diffusion coefficient was known, the molar concentration C0 can thus be determined from Eq. (2). With the α value of 285.8 sec-0.5, the average diffusion coefficient of 5.1×10-12 m2/sec, and the dilution factor of 676, the molar concentration of original polystyrene nanoparticle was determined to be 13 nM. In order to verify this value, we performed a gravimetric method, which used the total dry mass and average mass of single nanoparticle (r = 107 nm as determined by TEM) to calculate the molar concentration. Weighing method generated a molar concentration of 18 nM, which is in good agreement with the value from SPRM measurement. Note that, different from gravimetric method, the SPRM approach did not need the geometry of polystyrene nanoparticles, and SPRM approach was also suitable for nanoparticles with poly-dispersed distribution or irregular geometry, as it directly counted the number of nanoparticles. There are two major requirements in terms of the physical and chemical properties of the nanoparticles in order to utilize the present approach. First, the size of the polystyrene nanoparticles (refractive index = 1.55 - 1.6) should be no less than 150 nm in diameter to ensure a signal-to-background ratio of SPRM images captured at a high speed of 1000 frames per second. For those nanoparticles with higher refractive index (metal nanoparticles for instance), smaller nanoparticles are also applicable. Second, appropriate physical and chemical features of the nanoparticles are required to enable the permanent adsorption onto gold substrate with particular molecular modification. CONCLUSION We proposed a single nanoparticle counting method that was able to determine the absolute molar concentration of
nano-objects without calibration factors. This principle involved the semi-infinite diffusion model, as well as the distance-dependence feature of surface plasmon wave. From the former principle, hitting frequency was a function of the molar concentration and diffusion coefficient of nanoparticles. The later principle enabled the direct measurement of diffusion coefficient, so that the molar concentration can be determined. The present method does not require any prior knowledge regarding the size, density and chemical components of the nanoparticles. Moreover, the quantification was solely based on the physical constants (wavelength, incident angle, medium refractive index and Avogadro’s constant) and experimental parameters (area of observation region and the dilution factor). No calibration factor was involved, resulting in the absolute quantification without calibration. One additional opportunity offered by the present method was the existence of the interface, which can be functionalized to enable the physical (by charge or polarity) and chemical (by molecular interaction) selectivity to determine the target-of-interest in complicated samples. This is one advantage of counting nanoparticles at solution-substrate interface compared with counting in homogeneous solution. We believe that the present method could also play important roles in the measurement of precious samples with extremely low concentration or with nano-objects that have not been well-characterized yet.
ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. The detailed description of Eq. 1 and TEM information about polystyrene were provided in the Supporting Information (PDF)
AUTHOR INFORMATION Corresponding Author *E-mail:
[email protected] (W. W.)
Notes The authors declare no competing financial interest.
ACKNOWLEDGMENT We thank financial support from the National Natural Science Foundation of China (NSFC, Grant No. 21522503, 21405080, 21327008, 21327902), and the Natural Science Foundation of Jiangsu Province (BK20150013, BK20140592).
REFERENCES (1) Wagner, V.; Dullaart, A.; Bock, A.-K.; Zweck, A. Nat Biotech 2006, 24, 1211-1217. (2) Lee, J. H.; Yigit, M. V.; Mazumdar, D.; Lu, Y. Adv. Drug Del. Rev. 2010, 62, 592-605. (3) Ray, P. C. Chem. Rev. 2010, 110, 5332-5365. (4) Khandare, J.; Minko, T. Prog. Polym. Sci. 2006, 31, 359-397. (5) Shang, J.; Gao, X. Chem. Soc. Rev. 2014, 43, 7267-7278. (6) Haiss, W.; Thanh, N. T. K.; Aveyard, J.; Fernig, D. G. Anal. Chem. 2007, 79, 4215-4221. (7) Wang, W.; Tao, N. Anal. Chem. 2014, 86, 2-14. (8) Zhu, S.; Yang, L.; Long, Y.; Gao, M.; Huang, T.; Hang, W.;
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Yan, X. J. Am. Chem. Soc. 2010, 132, 12176-12178. (9) Bartczak, D.; Vincent, P.; Goenaga-Infante, H. Anal. Chem. 2015, 87, 5482-5485. (10) Liu, H.; Dong, C.; Ren, J. J. Am. Chem. Soc. 2014, 136, 2775-2785. (11) Yuan, Z.; Cheng, J.; Cheng, X.; He, Y.; Yeung, E. S. Analyst 2012, 137, 2930-2932. (12) Agrawal, A.; Zhang, C. Y.; Byassee, T.; Tripp, R. A.; Nie, S. M. Anal. Chem. 2006, 78, 1061-1070. (13) Xiao, X.; Fan, F.-R. F.; Zhou, J.; Bard, A. J. J. Am. Chem. Soc. 2008, 130, 16669-16677. (14) Boika, A.; Bard, A. J. Anal. Chem. 2015, 87, 4341-4346. (15) Han, G.; Xing, Z.; Dong, Y.; Zhang, S.; Zhang, X. Angew. Chem. Int. Ed. 2011, 50, 3462-3465. (16) Pace, H. E.; Rogers, N. J.; Jarolimek, C.; Coleman, V. A.; Higgins, C. P.; Ranville, J. F. Anal. Chem. 2011, 83, 9361-9369. (17) Degueldre, C.; Favarger, P. Y.; Wold, S. Anal. Chim. Acta 2006, 555, 263-268. (18) Laborda, F.; Jimenez-Lamana, J.; Bolea, E.; Castillo, J. R. J. Anal. At. Spectrom. 2013, 28, 1220-1232. (19) Wang, S.; Shan, X.; Patel, U.; Huang, X.; Lu, J.; Li, J.; Tao, N. Proc. Natl. Acad. Sci. 2010, 107, 16028-16032. (20) Huang, B.; Yu, F.; Zare, R. N. Anal. Chem. 2007, 79, 29792983. (21) Fang, Y.; Wang, W.; Wo, X.; Luo, Y.; Yin, S.; Wang, Y.; Shan, X.; Tao, N. J. Am. Chem. Soc. 2014, 136, 12584-12587. (22) Halpern, A. R.; Wood, J. B.; Wang, Y.; Corn, R. M. Acs Nano 2014, 8, 1022-1030. (23) Shan, X.; Fang, Y.; Wang, S.; Guan, Y.; Chen, H.-Y.; Tao, N. Nano Lett. 2014, 14, 4151-4157. (24) Cho, K.; Fasoli, J. B.; Yoshimatsu, K.; Shea, K. J.; Corn, R. M. Anal. Chem. 2015, 87, 4973-4979. (25) Shan, X.; Diez-Perez, I.; Wang, L.; Wiktor, P.; Gu, Y.; Zhang, L.; Wang, W.; Lu, J.; Wang, S.; Gong, Q.; Li, J.; Tao, N. Nat Nano 2012, 7, 668-672. (26) Fang, Y.; Chen, S.; Wang, W.; Shan, X.; Tao, N. Angew. Chem. Int. Ed. 2015, 54, 2538-2542.
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