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Analysis of SiO2 particle size using photon correlation spectroscopy
Optik 157 (2018) 259–266
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Analysis of SiO2 particle size using photon correlation spectroscopy Hyunki Kim, Jaeran Lee, Sok Won Kim ∗ Department of Physics, University of Ulsan, Ulsan 680-749, Korea
a r t i c l e
i n f o
Article history: Received 25 September 2017 Accepted 14 November 2017 Keywords: SiO2 Photon correlation spectroscopy Self-Assembly
a b s t r a c t In this study, fixed SiO2 particle sizes were observed using a photon correlation spectroscopy (PCS) system. PCS measurements were carried out using samples of fixed SiO2 particles uniformly dispersed on the surface of a cover glass and particles moving in a liquid. The monodispersed spherical SiO2 particles were made using the Stöber process with tetraethyl orthosilicate (TEOS) concentrations of 0.1 M, 0.2 M, and 0.3 M. The solid sample was made by fixing the particles on a cover glass by self-assembly, and the liquid sample was made by dispersing particles in distilled water. The fixed particle sizes on the surface were measured by PCS as 263.1 ± 21.7 nm, 309.3 ± 28.2 nm, and 425.4 ± 14.6 nm for TEOS concentrations of 0.1 M, 0.2 M, 0.3 M respectively. The corresponding liquid colloidal particle sizes were measured as 252.5 ± 8.0 nm, 322.8 ± 23.1 nm, and 423.2 ± 12.2 nm. The PCS show agreement with SEM images within ±9%. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Laser scanning confocal microscopy (LSCM) is used in biotechnology and industrial applications by their high resolution and ease of 3D imaging in visible light microscopy [1–4]. However, it is not suitable for analyzing particles on a surface with sizes of several tens of nanometers due to the diffraction limit of visible light. Therefore, LSCM is not usually used for surface analysis. Applicable alternatives include scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM). In particular, SEM has an advantage of having a depth of focus that is larger than that of an optical microscope. Therefore three-dimensional images with high magnification and high resolution can be obtained. But SEM has some restrictions, such as the need for surface treatment and use in a vacuum. To overcome these limitations, we designed a photon correlation spectroscopy (PCS) system based on confocal microscopy and analyzed the size of fixed particles on a surface and diffusing particles in a liquid. PCS is a technique for analyzing particle size ranging from a few micrometers to a few nanometers in a liquid state. The method involves statistical processing according to the Poisson distribution and measuring the intensity fluctuation of the scattered light from the particles. This technique is also known as dynamic light scattering (DLS) and quasi-elastic light scattering (QELS) [5,6]. This technique became a useful method for analysis of liquid colloidal samples by the progress in confocal microscope system, high efficiency photodetectors, and high resolution correlators in 1990’s [7–9]. PCS can be applied to measure the size of particles on a solid surface without information about the construction of the particles. It is also useful for systems of particles with different optical or physical properties [10–13]. The technique can also
∗ Corresponding author. E-mail address: [email protected] (S.W. Kim). https://doi.org/10.1016/j.ijleo.2017.11.085 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
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Fig. 1. Scattered light intensity fluctuation by the movement of (a) small-sized particles, (b) large-sized particles, (c) a large number of particles, and (d) a small number of particles in liquid.
Fig. 2. Scattered light intensity fluctuation by (a) large-sized particles, (b) small-sized particles, and (c) a large number of particles on a solid surface.
be used in biological, chemical, and physical applications and can analyze particle sizes of less than 1 nm. We developed a PCS system based on confocal microscopy and applied it to analyze fixed SiO2 particles on a surface and particles in a liquid colloidal state. The results were compared with that of SEM. 2. Theory Media such as polymer solutions or molten polymers have microscopic inhomogeneity. Therefore, light is scattered when it passes through the medium. The inhomogeneity originates from the density fluctuation caused by the thermal diffusion of molecules, which induces fluctuation of the scattered light intensity over time. PCS is a technique for measuring fluctuations in scattered light caused by variations in the number of particles in a fixed area, such as on the surface of a film. If the thickness and chemical composition of the film do not change, the effective focal area of incident light formed on the film surface can remain constant when the focal area is moved horizontally for measuring the fluctuation of scattered light. Information about the particles on the surface can then be obtained by analyzing the correlation function of the fluctuation of scattered light signal [14]. When light is incident on a micro-volume of liquid containing nanoparticles, the scattered light fluctuates over time, as shown in Fig. 1. When the particles are small, the period of fluctuation is short, as shown in Fig. 1(a). If only a few molecules are passing through the observation volume, the fluctuation intensity ıI is larger than the average intensity I, as shown in
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Fig. 3. Correlation function graph. For particles on a solid surface, g1 , g2 , and g3 are the scanning coefficients of the regions of the sample particles, substrate, and optical components, respectively. For samples in liquid, g1 , g2 , and g3 are the diffusion coefficients of the regions of sample particles, liquid flow, and optical components, respectively.
Fig. 1(c). These results from the diffusion of particles in the solution are the same as changes in light intensity produced by scanning particles on the surface of a thin film. When particles on the surface of a solid sample pass through the moving beam region, the intensity of scattering light fluctuates, as shown Fig. 2. If the surface particles are large, the scanning time of the incident light on a single particle increases, and the period of the light fluctuation is large. Let the intensity of light emitted at time t be I(t) and the intensity after time be I(t + ) in the focal observation region. The similarity between the two signals can be obtained through the autocorrelation function G(), which expresses the correlation between the signals obtained from the acquired time-series signals [15,16]: G() =
< ıI(t) · ıI(t + ) > < I(t)>2
(1)
where is the average light intensity for the whole time, and ıI(t) is the difference between and the measured light intensity at time t. ıI(t+ ) is the difference between and measured light intensity after time . To measure the size of SiO2 particles at that time, the correlation data were fitted using Eq. (2) [17]: G() =
1 · Xback · [(1 − 2 − 3 ) · g1 () + 2 · g2 () + 3 · g3 ()] N
(2)
where Xback is the background correlation intensity, N is the number of particles, i is the amplitude proportionality constant, and gi is the scanning coefficient (i = 1, 2, 3, each scanning region). Fig. 3 shows the correlation graph obtained by substituting the experimental data into Eq. (1). The graph is divided into scattered light from the SiO2 and that from other components. gi is the scanning coefficient for each scanning region of the scattered signal of the sample in the graph. When a nonlinear least square fit is performed for each diffusion region using Eq. (2), the exact identity of regions 1, 2, and 3 can be determined according to the experimental conditions. We can also obtain the characteristic time C for the region by fitting to Eq. (3) for the expression of the scanning coefficient gi () [18]:
−1
gi () = 1 + (/C )
(3)
At this time, particles on the surface do not diffuse, so C is considered as the characteristic time. The size of the scanning region, scanning speed, and characteristic time are used to calculate the average particle diameter on the surface of the fixed sample. The case of the liquid sample is slightly different. Generally, a commercial PCS system detects light emitted from the forward part of a circular cell and analyzes the average lifetime of the Brownian motion as a function of the scattering angle [10]. In this study, we developed a PCS system based on a confocal microscope that detects light scattered from the surface of a solid sample. This case is different from that of the general PCS equation, so we used a 3-dimensional diffusion model of particles used in fluorescence correlation spectroscopy (FCS) to determine the dynamic characteristics of particles using
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Fig. 4. Schematic diagram of DLS system.
the light scattered from a liquid colloidal sample, as shown in Eq. (4). This is applied to particles passing through the focal region of a 3D ellipsoid [19]:
gi () =
1 1 + /D
1/2
1 + 1/s
1
2
/D
(4)
where s is the shape constant of the focus, which is the length ratio s = z/w of the volume in the optical axis direction z and the beam waist direction radius w. D is the diffusion time. The parameters D and s can be obtained from the correlation function data measured from Eq. (4), and we can determine particle size. 3. Experiment Mono-dispersed spherical SiO2 particles were made using the Stöber process. The Stöber process is based on the hydrolysis and condensation reaction of tetraethyl orthosilicate (TEOS) with ammonia as a catalyst in a homogeneous solution of water and ethanol [20]. We used TEOS (98%), NH3 OH (28% NH3 in water), EtOH (99.9%), and distilled water. The SiO2 was made using TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M. The NH3 OH concentration was 0.7 M, and the ratio of EtOH to distilled water was 0.2. After stirring the solution of EtOH and water, it was mixed with a magnetic stirrer (300 rpm) for 2 h at room temperature while adding drops of TEOS at a constant rate. The reacting matter was allowed to mature for 24 h. The resulting liquid colloidal SiO2 particles were cleaned in distilled water using centrifugation at 10,000 rpm for 10 min, and impurities on the particle surfaces were eliminated using an ultrasonic cleaner. The solid sample was prepared by self-assembly. SiO2 solution was dropped on a cleaned cover glass, where it self-assembled as the distilled water dried at 100 ◦ C. The liquid colloidal sample was prepared by dispersing particles in distilled water. The PCS system was composed of a LSCM system based on one-photon excitation, as shown Fig. 4. The light source was a multiple-wavelength argon ion laser (MODU-LASER, Stellar-Pro ML/100). Light was passed through a 488-nm ND filter and two lenses of a beam expander. After reflection from a beam splitter, the light passed through a focusing lens and objective lens and was focused onto the sample on the cover glass. In the case of the solid sample, a perpendicular cross section of the focal volume is irradiated on the sample surface, and the light scattered by the sample particles in the focal volume returns to the objective lens. In the case of the liquid sample, the light in the focal volume of the liquid sample is scattered by moving particles. After the light passes through the focusing lens, beam splitter, and optical fiber (core diameter: 62.5 m), it reaches the detector of a single photon counting module (SPCM; id Quantiqe id100-MMF50). The photon signal is converted to an electric signal in the SPCM and then converted to a correlation function in a time-correlated single photon counter (TCSPC; PicoQuant, TimeHarp 260).
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Fig. 5. SEM images of the SiO2 films grown with TEOS concentrations of (a) 0.1 M (b) 0.2 M, and (c) 0.3 M.
Before measuring the size of fixed particles, the scanning rate was investigated by within the range of 100 Hz to 100,000 Hz to obtain a stable correlation graph. The correlation graph was the most stable at 10,000 Hz. Thus, this rate was used for the other experiments. We used a quickfit program to analyze the correlation graphs [21]. The characteristic time was obtained via the quickfit program in a region of the correlation function where a SiO2 particle passes through the focal volume. The scanning rate of the laser beam was calculated using the Galvano mirror scan speed and the size of the scanning region. The scanning region was obtained as 20.6 m × 30 m via confocal microscope imaging, and the scanning rate of the laser beam was determined as 1.05 mm/s at a Galvano mirror frequency of 10,000 Hz. This scanning rate was used to analyze the size of SiO2 particles with the characteristic time of the scanning region in the obtained correlation graph.
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Fig. 6. Correlation functions from fixed SiO2 particles uniformly dispersed on the surface of a cover glass.
Fig. 7. Normalized correlation functions from fixed SiO2 with TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M.
4. Results and discussion Fig. 5 shows SEM images of the self-assembled mono-dispersed spherical SiO2 samples made using the different TEOS concentrations. All fixed SiO2 particles had a spherical shape and equal size. The particle sizes were 262.0 ± 15.2 nm, 320.3 ± 11.5 nm, and 454.5 ± 13.5 nm at TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M, respectively. With increasing TEOS concentration, the size of the SiO2 increases because the monomer-induced growth of SiO2 increases with the concentration. Fig. 6 shows a graph of the correlation function of the light intensity variation caused by laser scanning on the surface of the solid sample. The function was averaged for data measured 10 times over a period of 120 s. The x-axis is the correlation delay time on a log scale, and the y-axis is the correlation coefficient for each delay time. The whole delay time () of 1 × 10−5 to 3 × 10 s was divided into three regions of scattered light from the SiO2 particles, substrate, and other optical components. The regions of the substrate and other optical components are induced from the properties of the substrate and the interference of light reflected from optical components, such as lenses, beam splitter, or objective. To obtain information about the SiO2 particles from the correlation function, the delay time region of 10−5 to 2 × 10−3 s was fitted with Eq. (3). To compare the correlation functions for each concentration, the functions were normalized as shown in Fig. 7. Fig. 7 shows the normalized correlation functions for TEOS concentrations of 0.1, 0.2, and 0.3 M. This figure shows a right shift below 1 × 10−3 s with increasing particle size caused by the TEOS concentration. The characteristic times obtained by Eq. (4) of the 2D model are 250.5 ± 20.7 s, 294.5 ± 26.9 s, and 405.2 ± 13.9 s at TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M, respectively. The size of the SiO2 particles was calculated using the characteristic time and the scanning rate of the focal volume on the sample surface. The obtained particle sizes were 263.1 ± 21.7 nm, 309.3 ± 28.2, and 0 425.4 ± 14.6 nm at TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M, respectively, which agreed with the SEM results within a range of ± 9%. Fig. 8 shows a correlation function of the scattered light intensity from liquid colloidal SiO2 particles. The x-axis and y-axis are the same as in Fig. 6. The function was averaged for the data measured 10 times over a period of 300 s. In the total delay time () of 10−5 to 3 × 10 s, the decay curve was divided into three regions of scattering by the SiO2 particles, background scattering by distilled water, and scattering by optical components. These results are different from those of the solid sample in Fig. 5. To obtain the particle size from the region of light scattered by the SiO2 particles, the correlation function was fitted with Eq. (4) in the range of 10−5 –5 × 10−3 s.
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Fig. 8. Correlation functions from SiO2 particles moving in liquid.
Fig. 9. Normalized correlation functions from SiO2 particles moving in liquid with TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M. Table 1 Particle sizes of SiO2 obtained by SEM and PCS from the surface of a film and in liquid Sample
Diameter (nm) SEM
0.1 M 0.2 M 0.3 M
262.0 ± 15.2 320.3 ± 11.5 454.5 ± 13.5
PCS Solid
Liquid
263.1 ± 21.7 309.3 ± 28.2 425.4 ± 14.6
252.5 ± 8.0 322.8 ± 23.1 423.2 ±12.2
Fig. 9 shows the normalized correlation function for each TEOS concentration. The graph also shifts to the right with increasing TEOS concentration at delay time below 1 × 10−3 s, as in the results of the solid sample in Fig. 7. By fitting to Eq. (2) of the 3D model, the diffusion times of SiO2 particles in liquid were measured as 1.79 ± 0.057 ms, 2.29 ± 0.164 ms, and 3.00 ± 0.086 ms at TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M, respectively. The size of the SiO2 particles was calculated from the diffusion time with the equation of Brownian diffusion. The obtained particle sizes were 252.5 ± 8.0 nm, 322.8 ± 23.1 nm, and 423.2 ± 12.2 nm at TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M, respectively. These results agree with the sizes from SEM and PCS obtained using the laser scanning method for fixed particles within ±9%, as shown in Table 1. Therefore, the PCS system can quickly and easily measure the particle size in solid and liquid samples. 5. Conclusion We developed a PCS system by combining LSCM and a correlation function analysis technique, and we measured the size of SiO2 particles made using TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M. The particle sizes were measured by obtaining the characteristic time of fixed particles and the diffusion time of diffusing particles in a liquid colloidal sample. The PCS results from liquid and solid samples are in agreement with the SEM results within about ±9%. Our PCS system can measure the size of SiO2 particles quickly and simply in solid and liquid states. Thus, the system can be applied to measure the size of particles on glass.
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Acknowledgment This work was supported by a grant from the National Research Foundation of Korea and funded by the Korean Government (No. NRD 2015R1D1A1A0106581). References [1] S.W. Paddock, Confocal laser scanning microscopy, Biotechniques 27 (1999) 992–1004. [2] S.W. Tsai, Y.Y. Chen, J.W. Liaw, Compound cellular imaging of laser scanning confocal microscopy by using gold nanoparticles and dyes, Sensors 8 (2008) 2306–2316. [3] L.P. Sung, J. Jasmin, X. Gu, T. Nguyen, J.W. Martin, Use of laser scanning confocal microscopy for characterizing changes in film thickness and local surface morphology of UV-exposed polymer coatings, J. Coat. Technol. 1 (4) (2004) 267–276. [4] M.I. Kang, D.H. Hong, T.S.M.W. Kim. Chu, S.W. Kim, Confocal laser scanning microscopy measurement of the morohology of vanadium pentoxide nanorods grown by electron beam irradiation of thermal oxidation, J. Nanophoton. 7 (1) (2012) 073797. [5] S.B. Dierker, R. Pindak, R.M. Fleming, I.K. Robinson, L. Berman, X-Ray photon correlation spectroscopy study of brownian motion of gold colloids in glycerol, Phys. Rev. Let 75 (1995) 449–452. [6] V.M. Gun’ko, A.V. Klyueva, Y.N. Levchuk, R. Leboda, Photon correlation spectroscopy investigations of proteins, Adv. Colloid. Interface Sci. 105 (2003) 201–328. [7] M. Zulauf, H.F. Eicke, Inverted micelles and microemulsions in the ternary system H2 O/aerosol-OT/isooctane as studied by photon correlation spectroscopy, J. Phys. Chem. 83 (4) (1979). [8] M. Filella, J. Zhang, M.E. Newman, J. Buffle, Analytical applications of photon correlation spectroscopy for size distribution measurements of natural colloidal suspensions: capabilities and limitations, Physicochem. Eng. Aspects 120 (1997) 27–46. [9] P.R. Dash, V. Toncheva, E. Schacht, L.W. Seymour, Synthetic polymers for vectorial delivery of DNA: characterisation of polymer-DNA complexes by photon correlation spectroscopy and stability to nuclease degradation and disruption by polyanions in vitro, J. Control. Release 48 (1997) 269–276. [10] R. Pecora, Dynamic light scattering measurement of nanometer particles in liquids, JNR 2 (2000) 123–131. [11] Q. Dai, X. Liu, J. Coutts, L. Austin, Q. Huo, A one-step highly sensitive method for DNA detection using dynamic light scattering, J. Am. Chem. Soc 130 (2008) 8138. [12] M. Zimbone, L. Calcagno, G. Messina, P. Baseri, G. Compagnini, Dynamic light scattering and UV–vis spectroscopy of gold nanoparticles solution, Mat. Lett. 65 (2011) 2906–2909. [13] H.S. Eom, I.H. Park, Measurement of polymer chain depletion layer in the poly(vinyl alcohol)/dimethyl sulfoxide/polystyrene latex system by dynamic light scattering, Poly. Korea 6 (2012) 628–636. [14] H. Kim, A. Ruhm, L.B. Luriof, J.K. Basuc, J. Lali, S.G.J. Mochriej, S.K. Sinha, X-ray photon correlation spectroscopy on polymer films with molecular weight dependence, Physica B. 336 (2003) 211–215. [15] O. Krichevsky, G. Bonnet, Fluorescence correlation spectroscopy: the technique and its applications, Rep. Prog. Phys. 65 (2002) 251–297. [16] P. Kask, P. Piksarv, M. Pooga, T. Mets, E. Lippmaa, Separation of the rotational contribution in fluorescence correlation experiments, Biophys. J. 55 (1989) 213–220. [17] J. Langowski, Protein-Protein interactions determined by fluorescence correlation spectroscopy, Methods Cell Biol. 85 (2008) 471–484. [18] G. Va´ımosi, A. Bodna´ır, G. Vereb, A. Jenei, C.K. Goldman§, J. Langowski, K. To´ıth, L. Ma´ıtyus, J. Szo¨ llo si, T.A. Waldmann, S. Damjanovich, IL-2 and IL-15 receptor ␣-subunits are coexpressed in a supramolecular receptor cluster in lipid rafts of T cells, PNAS 101 (30) (2004) 11082–11087. [19] D.R. Lide, CRC Handbook of Chemistry and Physics, CRC Press, 1994 (Chapter 6, p. 205). [20] Y.O, N. Kim, D. Shin, Effect of heat-treatment on the optical properties of self-Assembled SiO2 photonic crysctal, J. Kor. Ceram. Soc. 42 (2005) 127–131. [21] N. Baudendistel, G. Müller, W. Waldeck, P. Angel, J. Langowski, Two- hybrid fluorescence cross-Correlation spectroscopy detects protein–protein interactions in vivo, Chem. Phys. Chem. 6 (5) (2005) 984–990.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Analysis of SiO2 particle size using photon correlation spectroscopy Hyunki Kim, Jaeran Lee, Sok Won Kim ∗ Department of Physics, University of Ulsan, Ulsan 680-749, Korea
a r t i c l e
i n f o
Article history: Received 25 September 2017 Accepted 14 November 2017 Keywords: SiO2 Photon correlation spectroscopy Self-Assembly
a b s t r a c t In this study, fixed SiO2 particle sizes were observed using a photon correlation spectroscopy (PCS) system. PCS measurements were carried out using samples of fixed SiO2 particles uniformly dispersed on the surface of a cover glass and particles moving in a liquid. The monodispersed spherical SiO2 particles were made using the Stöber process with tetraethyl orthosilicate (TEOS) concentrations of 0.1 M, 0.2 M, and 0.3 M. The solid sample was made by fixing the particles on a cover glass by self-assembly, and the liquid sample was made by dispersing particles in distilled water. The fixed particle sizes on the surface were measured by PCS as 263.1 ± 21.7 nm, 309.3 ± 28.2 nm, and 425.4 ± 14.6 nm for TEOS concentrations of 0.1 M, 0.2 M, 0.3 M respectively. The corresponding liquid colloidal particle sizes were measured as 252.5 ± 8.0 nm, 322.8 ± 23.1 nm, and 423.2 ± 12.2 nm. The PCS show agreement with SEM images within ±9%. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Laser scanning confocal microscopy (LSCM) is used in biotechnology and industrial applications by their high resolution and ease of 3D imaging in visible light microscopy [1–4]. However, it is not suitable for analyzing particles on a surface with sizes of several tens of nanometers due to the diffraction limit of visible light. Therefore, LSCM is not usually used for surface analysis. Applicable alternatives include scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM). In particular, SEM has an advantage of having a depth of focus that is larger than that of an optical microscope. Therefore three-dimensional images with high magnification and high resolution can be obtained. But SEM has some restrictions, such as the need for surface treatment and use in a vacuum. To overcome these limitations, we designed a photon correlation spectroscopy (PCS) system based on confocal microscopy and analyzed the size of fixed particles on a surface and diffusing particles in a liquid. PCS is a technique for analyzing particle size ranging from a few micrometers to a few nanometers in a liquid state. The method involves statistical processing according to the Poisson distribution and measuring the intensity fluctuation of the scattered light from the particles. This technique is also known as dynamic light scattering (DLS) and quasi-elastic light scattering (QELS) [5,6]. This technique became a useful method for analysis of liquid colloidal samples by the progress in confocal microscope system, high efficiency photodetectors, and high resolution correlators in 1990’s [7–9]. PCS can be applied to measure the size of particles on a solid surface without information about the construction of the particles. It is also useful for systems of particles with different optical or physical properties [10–13]. The technique can also
∗ Corresponding author. E-mail address: [email protected] (S.W. Kim). https://doi.org/10.1016/j.ijleo.2017.11.085 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
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Fig. 1. Scattered light intensity fluctuation by the movement of (a) small-sized particles, (b) large-sized particles, (c) a large number of particles, and (d) a small number of particles in liquid.
Fig. 2. Scattered light intensity fluctuation by (a) large-sized particles, (b) small-sized particles, and (c) a large number of particles on a solid surface.
be used in biological, chemical, and physical applications and can analyze particle sizes of less than 1 nm. We developed a PCS system based on confocal microscopy and applied it to analyze fixed SiO2 particles on a surface and particles in a liquid colloidal state. The results were compared with that of SEM. 2. Theory Media such as polymer solutions or molten polymers have microscopic inhomogeneity. Therefore, light is scattered when it passes through the medium. The inhomogeneity originates from the density fluctuation caused by the thermal diffusion of molecules, which induces fluctuation of the scattered light intensity over time. PCS is a technique for measuring fluctuations in scattered light caused by variations in the number of particles in a fixed area, such as on the surface of a film. If the thickness and chemical composition of the film do not change, the effective focal area of incident light formed on the film surface can remain constant when the focal area is moved horizontally for measuring the fluctuation of scattered light. Information about the particles on the surface can then be obtained by analyzing the correlation function of the fluctuation of scattered light signal [14]. When light is incident on a micro-volume of liquid containing nanoparticles, the scattered light fluctuates over time, as shown in Fig. 1. When the particles are small, the period of fluctuation is short, as shown in Fig. 1(a). If only a few molecules are passing through the observation volume, the fluctuation intensity ıI is larger than the average intensity I, as shown in
H. Kim et al. / Optik 157 (2018) 259–266
261
Fig. 3. Correlation function graph. For particles on a solid surface, g1 , g2 , and g3 are the scanning coefficients of the regions of the sample particles, substrate, and optical components, respectively. For samples in liquid, g1 , g2 , and g3 are the diffusion coefficients of the regions of sample particles, liquid flow, and optical components, respectively.
Fig. 1(c). These results from the diffusion of particles in the solution are the same as changes in light intensity produced by scanning particles on the surface of a thin film. When particles on the surface of a solid sample pass through the moving beam region, the intensity of scattering light fluctuates, as shown Fig. 2. If the surface particles are large, the scanning time of the incident light on a single particle increases, and the period of the light fluctuation is large. Let the intensity of light emitted at time t be I(t) and the intensity after time be I(t + ) in the focal observation region. The similarity between the two signals can be obtained through the autocorrelation function G(), which expresses the correlation between the signals obtained from the acquired time-series signals [15,16]: G() =
< ıI(t) · ıI(t + ) > < I(t)>2
(1)
where
1 · Xback · [(1 − 2 − 3 ) · g1 () + 2 · g2 () + 3 · g3 ()] N
(2)
where Xback is the background correlation intensity, N is the number of particles, i is the amplitude proportionality constant, and gi is the scanning coefficient (i = 1, 2, 3, each scanning region). Fig. 3 shows the correlation graph obtained by substituting the experimental data into Eq. (1). The graph is divided into scattered light from the SiO2 and that from other components. gi is the scanning coefficient for each scanning region of the scattered signal of the sample in the graph. When a nonlinear least square fit is performed for each diffusion region using Eq. (2), the exact identity of regions 1, 2, and 3 can be determined according to the experimental conditions. We can also obtain the characteristic time C for the region by fitting to Eq. (3) for the expression of the scanning coefficient gi () [18]:
−1
gi () = 1 + (/C )
(3)
At this time, particles on the surface do not diffuse, so C is considered as the characteristic time. The size of the scanning region, scanning speed, and characteristic time are used to calculate the average particle diameter on the surface of the fixed sample. The case of the liquid sample is slightly different. Generally, a commercial PCS system detects light emitted from the forward part of a circular cell and analyzes the average lifetime of the Brownian motion as a function of the scattering angle [10]. In this study, we developed a PCS system based on a confocal microscope that detects light scattered from the surface of a solid sample. This case is different from that of the general PCS equation, so we used a 3-dimensional diffusion model of particles used in fluorescence correlation spectroscopy (FCS) to determine the dynamic characteristics of particles using
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Fig. 4. Schematic diagram of DLS system.
the light scattered from a liquid colloidal sample, as shown in Eq. (4). This is applied to particles passing through the focal region of a 3D ellipsoid [19]:
gi () =
1 1 + /D
1/2
1 + 1/s
1
2
/D
(4)
where s is the shape constant of the focus, which is the length ratio s = z/w of the volume in the optical axis direction z and the beam waist direction radius w. D is the diffusion time. The parameters D and s can be obtained from the correlation function data measured from Eq. (4), and we can determine particle size. 3. Experiment Mono-dispersed spherical SiO2 particles were made using the Stöber process. The Stöber process is based on the hydrolysis and condensation reaction of tetraethyl orthosilicate (TEOS) with ammonia as a catalyst in a homogeneous solution of water and ethanol [20]. We used TEOS (98%), NH3 OH (28% NH3 in water), EtOH (99.9%), and distilled water. The SiO2 was made using TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M. The NH3 OH concentration was 0.7 M, and the ratio of EtOH to distilled water was 0.2. After stirring the solution of EtOH and water, it was mixed with a magnetic stirrer (300 rpm) for 2 h at room temperature while adding drops of TEOS at a constant rate. The reacting matter was allowed to mature for 24 h. The resulting liquid colloidal SiO2 particles were cleaned in distilled water using centrifugation at 10,000 rpm for 10 min, and impurities on the particle surfaces were eliminated using an ultrasonic cleaner. The solid sample was prepared by self-assembly. SiO2 solution was dropped on a cleaned cover glass, where it self-assembled as the distilled water dried at 100 ◦ C. The liquid colloidal sample was prepared by dispersing particles in distilled water. The PCS system was composed of a LSCM system based on one-photon excitation, as shown Fig. 4. The light source was a multiple-wavelength argon ion laser (MODU-LASER, Stellar-Pro ML/100). Light was passed through a 488-nm ND filter and two lenses of a beam expander. After reflection from a beam splitter, the light passed through a focusing lens and objective lens and was focused onto the sample on the cover glass. In the case of the solid sample, a perpendicular cross section of the focal volume is irradiated on the sample surface, and the light scattered by the sample particles in the focal volume returns to the objective lens. In the case of the liquid sample, the light in the focal volume of the liquid sample is scattered by moving particles. After the light passes through the focusing lens, beam splitter, and optical fiber (core diameter: 62.5 m), it reaches the detector of a single photon counting module (SPCM; id Quantiqe id100-MMF50). The photon signal is converted to an electric signal in the SPCM and then converted to a correlation function in a time-correlated single photon counter (TCSPC; PicoQuant, TimeHarp 260).
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Fig. 5. SEM images of the SiO2 films grown with TEOS concentrations of (a) 0.1 M (b) 0.2 M, and (c) 0.3 M.
Before measuring the size of fixed particles, the scanning rate was investigated by within the range of 100 Hz to 100,000 Hz to obtain a stable correlation graph. The correlation graph was the most stable at 10,000 Hz. Thus, this rate was used for the other experiments. We used a quickfit program to analyze the correlation graphs [21]. The characteristic time was obtained via the quickfit program in a region of the correlation function where a SiO2 particle passes through the focal volume. The scanning rate of the laser beam was calculated using the Galvano mirror scan speed and the size of the scanning region. The scanning region was obtained as 20.6 m × 30 m via confocal microscope imaging, and the scanning rate of the laser beam was determined as 1.05 mm/s at a Galvano mirror frequency of 10,000 Hz. This scanning rate was used to analyze the size of SiO2 particles with the characteristic time of the scanning region in the obtained correlation graph.
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Fig. 6. Correlation functions from fixed SiO2 particles uniformly dispersed on the surface of a cover glass.
Fig. 7. Normalized correlation functions from fixed SiO2 with TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M.
4. Results and discussion Fig. 5 shows SEM images of the self-assembled mono-dispersed spherical SiO2 samples made using the different TEOS concentrations. All fixed SiO2 particles had a spherical shape and equal size. The particle sizes were 262.0 ± 15.2 nm, 320.3 ± 11.5 nm, and 454.5 ± 13.5 nm at TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M, respectively. With increasing TEOS concentration, the size of the SiO2 increases because the monomer-induced growth of SiO2 increases with the concentration. Fig. 6 shows a graph of the correlation function of the light intensity variation caused by laser scanning on the surface of the solid sample. The function was averaged for data measured 10 times over a period of 120 s. The x-axis is the correlation delay time on a log scale, and the y-axis is the correlation coefficient for each delay time. The whole delay time () of 1 × 10−5 to 3 × 10 s was divided into three regions of scattered light from the SiO2 particles, substrate, and other optical components. The regions of the substrate and other optical components are induced from the properties of the substrate and the interference of light reflected from optical components, such as lenses, beam splitter, or objective. To obtain information about the SiO2 particles from the correlation function, the delay time region of 10−5 to 2 × 10−3 s was fitted with Eq. (3). To compare the correlation functions for each concentration, the functions were normalized as shown in Fig. 7. Fig. 7 shows the normalized correlation functions for TEOS concentrations of 0.1, 0.2, and 0.3 M. This figure shows a right shift below 1 × 10−3 s with increasing particle size caused by the TEOS concentration. The characteristic times obtained by Eq. (4) of the 2D model are 250.5 ± 20.7 s, 294.5 ± 26.9 s, and 405.2 ± 13.9 s at TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M, respectively. The size of the SiO2 particles was calculated using the characteristic time and the scanning rate of the focal volume on the sample surface. The obtained particle sizes were 263.1 ± 21.7 nm, 309.3 ± 28.2, and 0 425.4 ± 14.6 nm at TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M, respectively, which agreed with the SEM results within a range of ± 9%. Fig. 8 shows a correlation function of the scattered light intensity from liquid colloidal SiO2 particles. The x-axis and y-axis are the same as in Fig. 6. The function was averaged for the data measured 10 times over a period of 300 s. In the total delay time () of 10−5 to 3 × 10 s, the decay curve was divided into three regions of scattering by the SiO2 particles, background scattering by distilled water, and scattering by optical components. These results are different from those of the solid sample in Fig. 5. To obtain the particle size from the region of light scattered by the SiO2 particles, the correlation function was fitted with Eq. (4) in the range of 10−5 –5 × 10−3 s.
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Fig. 8. Correlation functions from SiO2 particles moving in liquid.
Fig. 9. Normalized correlation functions from SiO2 particles moving in liquid with TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M. Table 1 Particle sizes of SiO2 obtained by SEM and PCS from the surface of a film and in liquid Sample
Diameter (nm) SEM
0.1 M 0.2 M 0.3 M
262.0 ± 15.2 320.3 ± 11.5 454.5 ± 13.5
PCS Solid
Liquid
263.1 ± 21.7 309.3 ± 28.2 425.4 ± 14.6
252.5 ± 8.0 322.8 ± 23.1 423.2 ±12.2
Fig. 9 shows the normalized correlation function for each TEOS concentration. The graph also shifts to the right with increasing TEOS concentration at delay time below 1 × 10−3 s, as in the results of the solid sample in Fig. 7. By fitting to Eq. (2) of the 3D model, the diffusion times of SiO2 particles in liquid were measured as 1.79 ± 0.057 ms, 2.29 ± 0.164 ms, and 3.00 ± 0.086 ms at TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M, respectively. The size of the SiO2 particles was calculated from the diffusion time with the equation of Brownian diffusion. The obtained particle sizes were 252.5 ± 8.0 nm, 322.8 ± 23.1 nm, and 423.2 ± 12.2 nm at TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M, respectively. These results agree with the sizes from SEM and PCS obtained using the laser scanning method for fixed particles within ±9%, as shown in Table 1. Therefore, the PCS system can quickly and easily measure the particle size in solid and liquid samples. 5. Conclusion We developed a PCS system by combining LSCM and a correlation function analysis technique, and we measured the size of SiO2 particles made using TEOS concentrations of 0.1 M, 0.2 M, and 0.3 M. The particle sizes were measured by obtaining the characteristic time of fixed particles and the diffusion time of diffusing particles in a liquid colloidal sample. The PCS results from liquid and solid samples are in agreement with the SEM results within about ±9%. Our PCS system can measure the size of SiO2 particles quickly and simply in solid and liquid states. Thus, the system can be applied to measure the size of particles on glass.
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