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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 23 — Nov. 5, 2012
  • pp: 25693–25699
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Improvement of photon correlation spectroscopy method for measuring nanoparticle size by using attenuated total reflectance

Victor Krishtop, Ivan Doronin, and Konstantin Okishev  »View Author Affiliations


Optics Express, Vol. 20, Issue 23, pp. 25693-25699 (2012)
http://dx.doi.org/10.1364/OE.20.025693


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Abstract

Photon correlation spectroscopy is an effective method for measuring nanoparticle sizes and has several advantages over alternative methods. However, this method suffers from a disadvantage in that its measuring accuracy reduces in the presence of convective flows of fluid containing nanoparticles. In this paper, we propose a scheme based on attenuated total reflectance in order to reduce the influence of convection currents. The autocorrelation function for the light-scattering intensity was found for this case, and it was shown that this method afforded a significant decrease in the time required to measure the particle sizes and an increase in the measuring accuracy.

© 2012 OSA

1. Introduction

Nanoparticles, which have been increasingly adopted in new and different areas of science and technology [1

1. Y.-C. Yeh, B. Creran, and V. M. Rotello, “Gold nanoparticles: preparation, properties, and applications in bionanotechnology,” Nanoscale 4(6), 1871–1880 (2012). [CrossRef] [PubMed]

14

14. F. L. Yap, P. Thoniyot, S. Krishnan, and S. Krishnamoorthy, “Nanoparticle cluster arrays for high-performance SERS through directed self-assembly on flat substrates and on optical fibers,” ACS Nano 6(3), 2056–2070 (2012). [CrossRef] [PubMed]

], exhibit behavior that dramatically depends on their size [15

15. B. Carl Englert, “Nanomaterials and the environment: uses, methods and measurement,” J. Environ. Monit. 9(11), 1154–1161 (2007). [CrossRef] [PubMed]

19

19. J. Qian, Z. Chen, J. Chen, Yu. Li, J. Xu, and Q. Sun, “Two-dimensional angularly selective optical properties of gold nanoshell with holes,” Opt. Express 20(13), 14614–14620 (2012). [CrossRef] [PubMed]

]. Different techniques for measuring the sizes of nanoparticles exist, such as electron transmittance microscopy [20

20. K. Maaz, The Transmission Electron Microscope (InTech, 2012).

], atomic force microscopy [21

21. V. Bellitto, Atomic Force Microscopy - Imaging, Measuring and Manipulating Surfaces at the Atomic Scale (InTech, 2012)

,22

22. B. Ruozi, G. Tosi, M. Tonelli, L. Bondioli, A. Mucci, F. Forni, and M. A. Vandelli, “AFM phase imaging of soft-hydrated samples: A versatile tool to complete the chemical-physical study of liposomes,” J. Liposome Res. 19(1), 59–67 (2009). [CrossRef] [PubMed]

], and other more exotic techniques such as those based on plasmonic resonance [23

23. B. Apter, O. Guilatt, and U. Efron, “Ring-type plasmon resonance in metallic nanoshells,” Appl. Opt. 50(28), 5457–5464 (2011). [CrossRef] [PubMed]

,24

24. K. Drozdowicz-Tomsia, H. T. Baltar, and E. M. Goldys, “Dense two-dimensional silver single and double nanoparticle arrays with plasmonic response in wide spectral range,” Langmuir 28(24), 9071–9081 (2012). [CrossRef] [PubMed]

]. One noteworthy method that has some advantages over other methods is photon correlation spectroscopy (PCS), which is sometimes also called dynamic light scattering [25

25. S.-M. Guo, J. He, N. Monnier, G. Sun, T. Wohland, and M. Bathe, “Bayesian approach to the analysis of fluorescence correlation spectroscopy data II: Application to simulated and in vitro data,” Anal. Chem. 84(9), 3880–3888 (2012). [CrossRef] [PubMed]

32

32. D. Salerno, D. Brogioli, F. Croccolo, R. Ziano, and F. Mantegazza, “Photon correlation spectroscopy with incoherent light,” Opt. Express 19(27), 26416–26422 (2011). [CrossRef] [PubMed]

]. The advantages of this method include high accuracy and high speed.

However, the accuracy of the PCS method is reduced by the presence of convective flows in the cell containing the medium under investigation. Such flows occur for reasons of thermal and concentration inhomogeneities of the medium, which are usually present for a long time (from several to tens of minutes) after loading the sample [33

33. V. I. Ivanov and K. N. Okishev, “Thermodiffusion mechanism of dynamic amplitude hologram recording in a two-component medium,” Tech. Phys. Lett. 32(11), 967–968 (2006). [CrossRef]

35

35. K. N. Okishev, V. I. Ivanov, S. V. Kliment'ev, A. A. Kuzin, and A. I. Livashvili, “The thermal diffusion mechanism of the nonlinear absorbing in nanoparticle suspensions,” Atmos. Oceanic Opt. 23(2), 106–107 (2010).

].

We propose the application of attenuated total reflectance (ATR) to the measurement scheme to reduce the dependence of the PCS results on these influences. In ATR, radiation that is incident on the boundary between two media at an angle greater than the critical angle partially penetrates into the second medium [36

36. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).

]. In the paper [37

37. K. H. Lan, N. Ostrowsky, and D. Sornette, “Brownian dynamics close to a wall studied by photon correlation spectroscopy from an evanescent wave,” Phys. Rev. Lett. 57(1), 17–20 (1986). [CrossRef] [PubMed]

], the authors used the scheme with ATR in PCS, and analytical expression for autocorrelation function (ACF) of scattered radiation in long and intermediate time range was found. Evanescent wavelets were used to observe the influence of anisotropy of diffusion close glass wall and sedimentation effects on autocorrelation function (ACF) [38

38. M. I. M. Feitosa and O. N. Mesquita, “Wall-drag effect on diffusion of colloidal particles near surfaces: a photon correlation study,” Phys. Rev. A 44(10), 6677–6685 (1991). [CrossRef] [PubMed]

,39

39. M. Hosoda, K. Sakai, and K. Takagi, “Measurement of anisotropic Brownian motion near an interface by evanescent light-scattering spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(5), 62756280–62756685 (1998). [CrossRef]

]. This technique has been applied for investigation of the dynamics of macromolecules close to wall [40

40. G. Fytas, S. H. Anastasiadis, R. Seghrouchni, D. Vlassopoulos, J. Li, B. J. Factor, W. Theobald, and C. Toprakcioglu, “Probing collective motions of terminally anchored polymers,” Science 274(5295), 2041–2044 (1996). [CrossRef] [PubMed]

,41

41. M. A. Plum, W. Steffen, G. Fytas, W. Knoll, and B. Menges, “Probing dynamics at interfaces: resonance enhanced dynamic light scattering,” Opt. Express 17(12), 10364–10371 (2009). [CrossRef] [PubMed]

]. In this study, a formula was derived for obtaining the ACF of the intensity of scattered radiation for a specific case, without considering the interaction between the particles and the wall of the cell. We then carried out numerical calculations, compared the results with those obtained through the traditional scheme and found some new features of ACF in a short time range that were not in the published literature.

2. Measurement scheme and mathematical model

PCS is based on an analysis of the light that is scattered by the Brownian particles. For the study of disperse systems, the theoretical dependence of the ACF of the scattered radiation, G(τ), is used [42

42. H. Z. Cummins and E. R. Pike, “Photon correlation and light beating spectroscopy,” NATO Advanced Study Institute Series, Volume B3 (Plenum Press, New York, 1974).

]:
G(τ)=Em22ek2Dτ,
(1)
where D is the Brownian diffusion coefficient of the particles, k is the scattering wave vector, and Em is the amplitude of the incident light wave.

Suppose light with a wavelength λ is incident on the boundary between media at an angle α that is larger than the critical angle for total internal reflection (Fig. 1
Fig. 1 Measurement scheme based on attenuated total reflection. 1 is the incident radiation, 2 is the scattered radiation, and 3 is a plot of the intensity of the transmitted radiation, I, versus the depth of penetration z.
).

The radiation in the second medium can be represented as a wave propagating along the interface in the plane of incidence with exponentially decaying amplitude along the z-axis. Hence, the phase difference between the origin (indicated by the point O in the Fig. 1) and the point (x, z) in the far field of the radiation scattered by a particle located at the origin can be written as
Δϕ=kxx+kzz,
(2)
where
kx=2πn1λsinα,
(3)
kz=2πn2λ.
(4)
We assume that the concentration of particles in suspension is low and that they are subject to Brownian motion. According to the Einstein–Smoluchowski theory for Brownian motion of particles [43

43. M. von Smoluchowski, “Zur kinetischen theorie der brownschen molekularbe-wegung und der suspensionen,” Ann. Physik (Leipzig) 21(326), 756–780 (1906). [CrossRef]

,44

44. A. Einstein, Investigations on the Theory of the Brownian Movement, (Dover Publications, Inc., 1956).

], the mean square displacement of a particle at time τ is
Δr2¯=2Dτ,
(5)
where D is the diffusion coefficient, determined by the ratio of the Einstein–Stokes equations [44

44. A. Einstein, Investigations on the Theory of the Brownian Movement, (Dover Publications, Inc., 1956).

]:
D=kbT6πηR,
(6)
where kb is the Boltzmann constant, T is the thermodynamic temperature, η is the coefficient of the dynamic viscosity of the fluid, and R is the radius of the particles.

The probability density of finding the particle at the point with coordinate x at time t + τ is normally distributed [45

45. S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15(1), 1–89 (1943). [CrossRef]

]:
Px=1σ2πe(xx0)2/2σ2,
(7)
where
σ2=σx2=σz2=13Δr2¯=23Dτ,
(8)
where x0 is the initial coordinate of the particle at time t. The anisotropic diffusion was observed [39

39. M. Hosoda, K. Sakai, and K. Takagi, “Measurement of anisotropic Brownian motion near an interface by evanescent light-scattering spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(5), 62756280–62756685 (1998). [CrossRef]

], but for simplification we suggested isotropic properties with respect to the direction of the interface plane, normal or parallel (σ = σx = σz).

We assume that the probability density along the z-axis is also subject to the normal distribution, but in this case, a reflection from the boundary between the two media is possible (Fig. 2
Fig. 2 Probability density plot showing the reflection from the boundary between the media.
). Hence, the probability can be written as the sum of the two components (z - z0) and (z + z0):

Pz=1σ2π(e(zz0)2/2σ2+e(z+z0)2/2σ2).
(9)

The additive to amplitude of the electric field of the perpendicularly scattered radiation (Fig. 1)including the light attenuation from penetration into the second medium for heterodyne detectioncan be written as
E=E0ez/b0cos(kxx+kzz),
(10)
where b0=λ2πn1/sin2α(n2n1)2 is the depth of penetration [36

36. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).

] and E0 is the amplitude of the electric field of the incident radiation. Therefore, at the initial time t0,
Et0=E0ez0/b0cos(kxx0+kzz0).
(11)
To simplify the problem, we perform the substitution
u=xx0,ϕx=kxx0.
(12)
Using Eq. (12), Eqs. (10) and (11) are converted to the forms
E=E0ez/b0cos(kxu+ϕx+kzz),
(13)
Et0=E0ez0/b0cos(ϕx+kzz0).
(14)
Consequently, we can write the expression for the autocorrelation function of scattered light G(τ) in the form
G(τ)=E02π00+02πPzPxe(zz0)/b0cos(ϕx+kzz0)cos(kxu+ϕx+kzz)dϕxdudzdz0.
(15)
After integration of Eq. (15) with respect to dφx and du, we obtain
G(τ)=E02ekx2σ2/2σ2π00[e(zz0)2/2σ2+e(z+z0)2/2σ2]e(z+z0)/b0cos(kz(zz0))dzdz0.
(16)
Using Eq. (8), Eq. (16) can be rewritten as

G(τ)=E02ekx2Dτ/32πDτ/300[e3(zz0)2/4Dτ+e3(z+z0)2/4Dτ]e(z+z0)/b0cos(kz(zz0))dzdz0.
(17)

Equation (17) is then solved numerically using the mathematical simulation package MATLAB. Calculations were performed for radiation with a wavelength of λ = 1550 nm incident at an angle of α = 85° on the interface between the glass (n1 = 1.54) and the suspension (n2 = 1.33) of the spherical nanoparticles.

3. Results and discussions

Figure 3
Fig. 3 Normalized autocorrelation function of the scattered radiation obtained using the scheme based on ATR (curve 1) and the traditional scheme (curve 2).
shows the normalized autocorrelation function of scattered light g(τ) obtained using the scheme based on ATR (curve 1) calculated in arbitrary coordinates Dτ, where D is the diffusion coefficient of the spherical nanoparticles from Eq. (6). For comparison, the Fig. 3 also shows the normalized autocorrelation function obtained using the traditional scheme (curve 2). The autocorrelation function obtained using the ATR-based scheme markedly deviates from that obtained using the traditional scheme for small values of Dτ. In this regime, the autocorrelation function obtained using the ATR-based scheme is inversely proportional to Dτ, although for large values of Dτ, its character is similar to the autocorrelation function obtained using the traditional scheme. Figure 4
Fig. 4 Normalized autocorrelation function of scattered radiation obtained using the scheme based on ATR for spherical particles with radii of 1 nm (curve 1), 10 nm (curve 2), and 100 nm (curve 3).
shows plots of g(τ), calculated for spherical particles with radii of 1, 10, and 100 nm, yielding curves 1, 2, and 3, respectively. As shown, the function has a different character in the short-time range for all particle sizes, which suggests that this scheme can be used to measure a wide range of nanoparticle sizes and that it has a speed advantage over traditional measurement schemes.

4. Conclusion

We proposed a scheme based on attenuated total reflectance in order to reduce the influence of convection currents in PCS measurements. To this end, we derived an expression for the autocorrelation function for the light-scattering intensity of the scattered radiation. Numerical calculations show that the short-time range form of the function differs significantly from that of the function for the traditional measurement scheme. In addition, for particles of different radii (1, 10, and 100 nm), the function has a different character in the short-time range, which suggests that this scheme can be used to measure the size of nanoparticles and that it has a speed advantage over traditional measurement schemes. Note however that our analysis in this paper does not take into account the effects of particle interaction with the cell walls (e.g., attachment of particles to the walls), which may impose some restrictions on the use of the measurement scheme.

Acknowledgments

This research has been conducted with funding from the Research Grant of Kwangwoon University in 2012.

References and links

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2.

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L. Xiao, L. Gu, S. B. Howell, and M. J. Sailor, “Porous silicon nanoparticle photosensitizers for singlet oxygen and their phototoxicity against cancer cells,” ACS Nano 5(5), 3651–3659 (2011). [CrossRef] [PubMed]

7.

R. Intartaglia, K. Bagga, F. Brandi, G. Das, A. Genovese, E. Di Fabrizio, and A. Diaspro, “Optical properties of femtosecond laser-synthesized silicon nanoparticles in deionized water,” J. Phys. Chem. C 115(12), 5102–5107 (2011). [CrossRef]

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D. Kovalev and M. Fujii, “Silicon nanocrystals: photosensitizers for oxygen molecules,” Adv. Mater. (Deerfield Beach Fla.) 17(21), 2531–2544 (2005). [CrossRef]

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R. Intartaglia, K. Bagga, M. Scotto, A. Diaspro, and F. Brandi, “Luminescent silicon nanoparticles prepared by ultra short pulsed laser ablation in liquid for imaging applications,” Opt. Mater. Express 2(5), 510–518 (2012). [CrossRef]

12.

D. S. Filonov, A. E. Krasnok, A. P. Slobozhanyuk, P. V. Kapitanova, E. A. Nenasheva, Y. S. Kivshar, and P. A. Belov, “Experimental verification of the concept of all-dielectric nanoantennas,” Appl. Phys. Lett. 100(20), 201113 (2012). [CrossRef]

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H. Alaeian and J. A. Dionne, “Plasmon nanoparticle superlattices as optical-frequency magnetic metamaterials,” Opt. Express 20(14), 15781–15796 (2012). [CrossRef] [PubMed]

14.

F. L. Yap, P. Thoniyot, S. Krishnan, and S. Krishnamoorthy, “Nanoparticle cluster arrays for high-performance SERS through directed self-assembly on flat substrates and on optical fibers,” ACS Nano 6(3), 2056–2070 (2012). [CrossRef] [PubMed]

15.

B. Carl Englert, “Nanomaterials and the environment: uses, methods and measurement,” J. Environ. Monit. 9(11), 1154–1161 (2007). [CrossRef] [PubMed]

16.

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Nonlinear control of invisibility cloaking,” Opt. Express 20(14), 14954–14959 (2012). [CrossRef] [PubMed]

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J. Qian, Z. Chen, J. Chen, Yu. Li, J. Xu, and Q. Sun, “Two-dimensional angularly selective optical properties of gold nanoshell with holes,” Opt. Express 20(13), 14614–14620 (2012). [CrossRef] [PubMed]

20.

K. Maaz, The Transmission Electron Microscope (InTech, 2012).

21.

V. Bellitto, Atomic Force Microscopy - Imaging, Measuring and Manipulating Surfaces at the Atomic Scale (InTech, 2012)

22.

B. Ruozi, G. Tosi, M. Tonelli, L. Bondioli, A. Mucci, F. Forni, and M. A. Vandelli, “AFM phase imaging of soft-hydrated samples: A versatile tool to complete the chemical-physical study of liposomes,” J. Liposome Res. 19(1), 59–67 (2009). [CrossRef] [PubMed]

23.

B. Apter, O. Guilatt, and U. Efron, “Ring-type plasmon resonance in metallic nanoshells,” Appl. Opt. 50(28), 5457–5464 (2011). [CrossRef] [PubMed]

24.

K. Drozdowicz-Tomsia, H. T. Baltar, and E. M. Goldys, “Dense two-dimensional silver single and double nanoparticle arrays with plasmonic response in wide spectral range,” Langmuir 28(24), 9071–9081 (2012). [CrossRef] [PubMed]

25.

S.-M. Guo, J. He, N. Monnier, G. Sun, T. Wohland, and M. Bathe, “Bayesian approach to the analysis of fluorescence correlation spectroscopy data II: Application to simulated and in vitro data,” Anal. Chem. 84(9), 3880–3888 (2012). [CrossRef] [PubMed]

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32.

D. Salerno, D. Brogioli, F. Croccolo, R. Ziano, and F. Mantegazza, “Photon correlation spectroscopy with incoherent light,” Opt. Express 19(27), 26416–26422 (2011). [CrossRef] [PubMed]

33.

V. I. Ivanov and K. N. Okishev, “Thermodiffusion mechanism of dynamic amplitude hologram recording in a two-component medium,” Tech. Phys. Lett. 32(11), 967–968 (2006). [CrossRef]

34.

K. Okishev and I. Doronin, “Application of photon correlation spectroscopy for investigation of silica nanospheres suspension,” Bull. Sci. Res. 14, edited by V. Stroganov, Khabarovsk, Russia, FESTU, 4–8 (2010).

35.

K. N. Okishev, V. I. Ivanov, S. V. Kliment'ev, A. A. Kuzin, and A. I. Livashvili, “The thermal diffusion mechanism of the nonlinear absorbing in nanoparticle suspensions,” Atmos. Oceanic Opt. 23(2), 106–107 (2010).

36.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).

37.

K. H. Lan, N. Ostrowsky, and D. Sornette, “Brownian dynamics close to a wall studied by photon correlation spectroscopy from an evanescent wave,” Phys. Rev. Lett. 57(1), 17–20 (1986). [CrossRef] [PubMed]

38.

M. I. M. Feitosa and O. N. Mesquita, “Wall-drag effect on diffusion of colloidal particles near surfaces: a photon correlation study,” Phys. Rev. A 44(10), 6677–6685 (1991). [CrossRef] [PubMed]

39.

M. Hosoda, K. Sakai, and K. Takagi, “Measurement of anisotropic Brownian motion near an interface by evanescent light-scattering spectroscopy,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(5), 62756280–62756685 (1998). [CrossRef]

40.

G. Fytas, S. H. Anastasiadis, R. Seghrouchni, D. Vlassopoulos, J. Li, B. J. Factor, W. Theobald, and C. Toprakcioglu, “Probing collective motions of terminally anchored polymers,” Science 274(5295), 2041–2044 (1996). [CrossRef] [PubMed]

41.

M. A. Plum, W. Steffen, G. Fytas, W. Knoll, and B. Menges, “Probing dynamics at interfaces: resonance enhanced dynamic light scattering,” Opt. Express 17(12), 10364–10371 (2009). [CrossRef] [PubMed]

42.

H. Z. Cummins and E. R. Pike, “Photon correlation and light beating spectroscopy,” NATO Advanced Study Institute Series, Volume B3 (Plenum Press, New York, 1974).

43.

M. von Smoluchowski, “Zur kinetischen theorie der brownschen molekularbe-wegung und der suspensionen,” Ann. Physik (Leipzig) 21(326), 756–780 (1906). [CrossRef]

44.

A. Einstein, Investigations on the Theory of the Brownian Movement, (Dover Publications, Inc., 1956).

45.

S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15(1), 1–89 (1943). [CrossRef]

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(290.0290) Scattering : Scattering
(300.0300) Spectroscopy : Spectroscopy

ToC Category:
Spectroscopy

History
Original Manuscript: August 8, 2012
Revised Manuscript: October 12, 2012
Manuscript Accepted: October 22, 2012
Published: October 29, 2012

Citation
Victor Krishtop, Ivan Doronin, and Konstantin Okishev, "Improvement of photon correlation spectroscopy method for measuring nanoparticle size by using attenuated total reflectance," Opt. Express 20, 25693-25699 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-23-25693


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References

  1. Y.-C. Yeh, B. Creran, and V. M. Rotello, “Gold nanoparticles: preparation, properties, and applications in bionanotechnology,” Nanoscale4(6), 1871–1880 (2012). [CrossRef] [PubMed]
  2. Y. N. Kulchin, A. V. Bezverbny, O. A. Bukin, S. S. Voznesensky, S. S. Golik, A. Y. Mayor, Y. A. Shchipunov, and I. G. Nagorny, “Nonlinear optical properties of biomineral and biomimetical nanocomposite structures,” Laser Phys.21(3), 630–636 (2011). [CrossRef]
  3. M. De, P. S. Ghosh, and V. M. Rotello, “Applications of nanoparticles in biology,” Adv. Mater. (Deerfield Beach Fla.)20(22), 4225–4241 (2008). [CrossRef]
  4. V. Rotello, Nanoparticle: Building Blocks for Nanotechnology (Springer, 2004).
  5. F. Erogbogbo, K. T. Yong, I. Roy, R. Hu, W. C. Law, W. Zhao, H. Ding, F. Wu, R. Kumar, M. T. Swihart, and P. N. Prasad, “In vivo targeted cancer imaging, sentinel lymph node mapping and multi-channel imaging with biocompatible silicon nanocrystals,” ACS Nano5(1), 413–423 (2011). [CrossRef] [PubMed]
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