RU2502980C1 - Method of determining concentration and average size of nanoparticles in sol - Google Patents

Abstract

FIELD: nanotechnology.SUBSTANCE: reference samples with the predetermined initial concentration of nanoparticles are produced. Infrared spectra of the reference samples are recorded, the characteristic absorption peaks are identified. The infrared spectra of the reference samples are recorded during the coagulation process, the experimental dependence of the transmission coefficient of infrared radiation is created on the basis of the coagulation time. The infrared spectra of the reference samples are recorded and the concentrations C and the size of the nanoparticles d are determined according to the relationswhere Cis the initial concentration of the nanoparticles in the sol, K is the coagulation constant determined by the sol composition; ?is the density of the sol component forming the nanoparticles; Vis the volume of the sol component forming the nanoparticles; Nis the Avogadro's number; Mis the molar mass of the sol component forming the nanoparticles; Uis the amount of the sol; k is the Boltzmann constant; T=29S K is the temperature; ? is the dynamic viscosity of the solution; ?=10is the parameter characterising the effective probability of collision of the nanoparticles with each other; ? is the size of the molecule forming the nanoparticle; ?=3 is growth coefficient in the diameter of the nanoparticle in the coagulation process; ?=13 is the constant related to the fractality of the nanoparticle; ?(T) is the approximation of the experimental dependence of the transmission coefficient of infrared radiation through the sol on the basis of time.EFFECT: creation of the method of determining the concentration and the average size of nanoparticles in sol undergoing coagulation by IR-spectroscopy.14 dwg

Description

The proposed method relates to the field of determining the concentration and average size of nanoparticles in a sol undergoing coagulation using infrared spectroscopy (IR spectroscopy).

The closest in technical essence to the proposed solution is a method for determining the average aggregate size of the filler particles, their concentration and distribution in the volume of the polymer matrix [1]. It consists in the production of reference samples, recording the IR transmission spectra of the reference samples, identifying the extrema of the spectrograms of the reference samples in accordance with the average particle size of the filler, their concentration and distribution, constructing calibration graphs, then recording the IR spectra of the studied samples and comparing the extremes of the spectrograms of the studied samples with a calibration graph.

The disadvantage of this method is the need for preliminary determination of the average size of the aggregates of the filler particles, their concentration and distribution using an electron microscope, in addition, this method does not allow to determine the concentration and size of the nanoparticles in the ash.

The technical result of the present invention is that by means of IR spectroscopy, the average particle size and their concentration in the ash undergoing coagulation is determined.

The essence of the proposed method lies in the fact that the manufactured reference samples with a given initial concentration of nanoparticles; infrared spectra (IR spectra) of transmission of reference samples are recorded; characteristic absorption peaks are identified; the experimental dependence of the IR transmittance on the initial concentration of nanoparticles is built; IR spectra of reference samples are recorded during the coagulation process; the experimental dependence of the IR transmittance on the coagulation time is built; IR spectra of the studied samples are recorded and the concentration (C) and average nanoparticle size (d) are determined by the ratios:

$$C\left(T\right)=\frac{{\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="00000024.png,00000025.png"\; state="\{\{state\}\}">C</figure-callout>}}_0}{\mathrm{one}+{\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="00000024.png,00000025.png"\; state="\{\{state\}\}">C</figure-callout>}}_0\tau \left(T\right)K},\left(\mathrm{one}\right)$$

$$d\left(T\right)=\alpha {\chi }^{\frac{\ln \left(\mathrm{one}+K\cdot {\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="00000024.png,00000025.png"\; state="\{\{state\}\}">C</figure-callout>}}_0\cdot \tau \left(T\right)\right)}{\ln \left(\xi \right)}},\left(2\right)$$

$${\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="00000024.png,00000025.png"\; state="\{\{state\}\}">C</figure-callout>}}_0=\frac{{\rho }_{\mathrm{to}}{V}_{\mathrm{to}}{N}_A}{M_{\mathrm{to}}{V}_{s\mathrm{about}l\mathrm{I\; am}}},\left(3\right)$$

$$K=\frac{\mathrm{four}\mathrm{<figure-callout\; id="3"\; label="k\; T"\; filenames="00000025.png,00000027.png"\; state="\{\{state\}\}">k\; </figure-callout>}T}{3\eta }\psi ,\left(\mathrm{four}\right)$$

where Co is the initial concentration of nanoparticles in the ash; K is the coagulation constant determined by the composition of the sol; ρ _to is the density of the sol component forming the nanoparticles; V _to is the volume of the sol component forming the nanoparticles; N _A is the Avogadro number; M _to - the molar mass of the sol component forming the nanoparticles; V _sol - the volume of the sol; k is the Boltzmann constant; T = 29SK is the temperature; η is the dynamic viscosity of the solution; ψ = 10 ^-9 is a parameter characterizing the effective probability of collision of nanoparticles with each other; α is the size of the molecule forming the nanoparticle; χ = 3 is the coefficient of growth of the diameter of the nanoparticles during coagulation; ξ = 13 is a constant associated with the fractality of the nanoparticle; τ (T) is an approximation of the experimental time dependence of the transmittance of infrared radiation through a sol.

определяет число молекул в наночастице с течением времени; эффективная вероятность соударения достаточно малая величина (ψ=10^-13); число молекул в наночастице линейно растет с течением времени при заданной постоянной температуре. Соотношение (3) определяет начальную концентрацию наночастиц исходя из объема компонентов золя. Соотношение (4) представляет собой константу коагуляции и зависит только от состава золя. Соотношение (2) характеризует фрактальную структуру наночастиц [3] и учитывает, что в процессе коагуляции на каждом этапе участвует ξ=13 составных частиц, причем коэффициент роста диаметра наночастицы на следующем этапе будет составлять χ=3.Relation (1) is a solution to the Smoluchowski equation [2] and takes into account that the initial size of one nanoparticle in the ash corresponds to the size of one molecule (α); value $$\frac{C_0}{C}$$

determines the number of molecules in a nanoparticle over time; the effective probability of collision is quite small (ψ = 10 ^-13 ); the number of molecules in a nanoparticle increases linearly over time at a given constant temperature. Relation (3) determines the initial concentration of nanoparticles based on the volume of sol components. Relation (4) is a coagulation constant and depends only on the composition of the sol. Relation (2) characterizes the fractal structure of nanoparticles [3] and takes into account that ξ = 13 composite particles participate in the coagulation process at each stage, and the coefficient of growth of the nanoparticle diameter at the next stage will be χ = 3.

This combination of experimental and theoretical data allows us to determine the concentration and average size of nanoparticles in the ash using IR spectroscopy.

An example of the method. Determination of the concentration and average size of nanoparticles in orthosilicic acid ash.

1. The manufacture of reference samples with a given initial concentration of nanoparticles (C ₀ ). The salt of orthosilicic acid was prepared in two stages, at the first stage tetraethoxysilane and ethyl alcohol were mixed, then at the second stage distilled water was introduced into the resulting solution. The initial concentration of nanoparticles in the ash of orthosilicic acid was determined by the ratio (3), varying the volume of tetraethoxysilane and alcohol.

2. Recording IR transmission spectra of reference samples. The IR spectra of the orthosilicic acid sol were recorded using an FSM 1201 IR Fourier spectrometer (EuroLab) using an attachment for multiple total internal reflection disturbance (MNVPO).

Figure 1 presents the IR transmission spectra of the sol of orthosilicic acid in the spectral range (650-4450) cm ^-1 at different initial concentrations of nanoparticles (C ₀ ): curve 1 - 2.023 · 10 ²⁷ m ^-3 ; curve 2 - 1.798 · 10 ²⁷ m ^-3 ; curve 3 - 1.349 · 10 ²⁷ m ^-3 ; curve 4 - 8.992 · 10 ²⁶ m ^-3 ; curve 5 - 6.744 · 10 ²⁶ m ^-3 ; curve 6 - 2.697 · 10 ²⁶ m ^-3 .

3. Identification of characteristic absorption peaks. Since the nanoparticles in the test ash are formed by orthosilicic acid (Si (OH) ₄ ), we will use the absorption peak at 965 cm ^-1 (Fig. 1), which characterizes the stretching vibrations of Si-OH bonds.

Figure 2 presents the IR transmission spectra of the sol of orthosilicic acid in the spectral range (900-1000) cm ^-1 at different initial concentrations of nanoparticles (C ₀ ): curve 1 - 2.023 · 10 ²⁷ m ^-3 ; curve 2 - 1.798 · 10 ²⁷ m ^-3 ; curve 3 - 1.349 · 10 ²⁷ m ^-3 ; curve 4 - 8.992 · 10 ²⁶ m ^-3 ; curve 5 - 6.744 · 10 ²⁶ m ^-3 ; curve 6 - 2.697 · 10 ²⁶ m ^-3 .

4. Construction of an experimental dependence of the transmittance of infrared radiation (7) on the initial concentration of nanoparticles (C ₀ ).

Figure 3 shows the dependence of the transmittance of infrared radiation (7) through a sol of orthosilicic acid on the initial concentration of nanoparticles (C ₀ ): curve 1 - experimental data; curve 2 - approximation by an exponential function.

5. Recording IR spectra of reference samples during the coagulation process. The coagulation process of the sol of orthosilicic acid was started by adding hydrochloric acid (HCl), acting as a catalyst. The IR spectra of the orthosilicic acid sol were recorded using an FSM 1201 IR Fourier spectrometer (EuroLab) using an attachment for multiple total internal reflection disturbance (MNVPO).

Figure 4 and figure 5 presents the IR transmission spectra of the sol of orthosilicic acid in the spectral range 650-4450 cm ^-1 (figure 4) and 900-1000 cm ^-1 (figure 5) with an initial concentration of nanoparticles (C ₀ = 1.349 · 10 ²⁷ m ^-3 ) at different coagulation times: curve 1 - before the start of the process; curve 2 - 5 s; curve 3 - 30 s; curve 4-1 min; curve 5-2 min; curve 6 - 6 min; curve 7 - 10 min; curve 8 - 20 min; curve 9 - 30 min; curve 10 - 40 min; curve 11 - 50 min; curve 12 - 60 minutes

Fig.6 and Fig.7 shows the IR transmission spectra of the sol of orthosilicic acid in the spectral range (650-4450) cm ^-1 (Fig.6) and (900-1000) cm ^-1 (Fig.7) with an initial concentration of nanoparticles C ₀ = 8.992 · 10 ²⁶ m ^-3 at different coagulation times: curve 1 - before the start of the process; curve 2 - 5 s; curve 3 - 30 s; curve 4 - 1 min; curve 5 - 2 min; curve 6 - 6 min; curve 7 - 10 min; curve 8 - 20 min; curve 9 - 30 min; curve 10 - 40 min; curve 11 - 50 min; curve 12 - 60 minutes

6. Construction of an experimental dependence of the transmittance (7) of IR radiation on the coagulation time (t);

On Fig presents the dependence of the transmittance of infrared radiation through a sol of orthosilicic acid from the coagulation time: curve 1 - experimental data at an initial concentration of nanoparticles (C ₀ = 8.992 · 10 ²⁶ m ^-3 ); curve 2 - experimental data at an initial concentration of nanoparticles (C ₀ = 1.349 · 10 ²⁷ m ^-3 ); curve 3 and 4 - approximation by a power function of the form:

$$T\left(\tau \right)=a{\tau }^b+{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="00000024.png,00000025.png"\; state="\{\{state\}\}">T</figure-callout>}}_0,\left(5\right)$$

$$T\left(\tau \right)={\left(\frac{T-T_0}{a}\right)}^{\frac{\mathrm{one}}{b}},\left(6\right)$$

where a = 2,236 · 10 ^-3 , b = 0,5 - some constants; T ₀ is the transmittance of infrared radiation through a sol of orthosilicic acid before the start of the coagulation process at various initial concentrations of nanoparticles (at C ₀ = 8.992 · 10 ²⁶ m ^-3 -T ₀ = 0.127; at C ₀ = 1.349 · 10 ²⁷ m ^-3 -T ₀ = 0.072).

Figures 9 and 10 show the dependences of the concentration of nanoparticles (C) in the orthosilicic acid sol on the IR transmission coefficient (7) through the sol obtained by the relations (1), (3), (4), (6), at different initial concentrations of nanoparticles, C ₀ = 1.349 · 10 ²⁷ m ^-3 (Fig. 9) and C ₀ = 8.992 · 10 ²⁶ m ^-3 (Fig. 10).

In Fig.11 and Fig.12 presents the dependence of the size of the nanoparticles (d) in the sol of orthosilicic acid on the transmittance of PC radiation (7) through the sol obtained by the relations (2), (3), (4), (6), at different initial concentrations of nanoparticles, C ₀ = 1.349 · 10 ²⁷ m ^-3 (11) and C ₀ = 8.992 · 10 ²⁶ m ^-3 (fit 12).

7. Recording IR spectra of the test sample. The PC spectra of the studied sol of orthosilicic acid were recorded using an FSM 1201 FTIR spectrometer (EuroLab) using an attachment for multiple violation of total internal reflection (MNPVO)

On Fig presents the infrared transmission spectrum of the investigated sol of orthosilicic acid with an initial concentration of nanoparticles (With ₀ = 1,349 · 10 ²⁷ m ^-3 ). The transmittance of PC radiation (7) through the sol at the absorption peaks of 965 cm ^-1 is equal to 0.089.

8. Determination of the concentration and size of nanoparticles by the ratio (1), (2), (4) and (6). For the sol of orthosilicic acid η = l, 096 · 10 ^-3 Pa · s, α = 2 nm.

$$K=\frac{\mathrm{four}\cdot 1.38\cdot {10}^{-23}\frac{D\mathrm{well}}{\mathrm{TO}}\cdot 298\mathrm{TO}}{3\cdot \mathrm{1,096}P\mathrm{but}\cdot \mathrm{from}}\cdot {10}^{-9}=\mathrm{5,005}\cdot {10}^{-27}\frac{{\mathrm{<figure-callout\; id="3"\; label="m"\; filenames="00000025.png,00000027.png"\; state="\{\{state\}\}">m</figure-callout>}}^3}{\mathrm{from}}\left(7\right)$$

$$\mathrm{FROM}=\frac{\mathrm{1,349}\cdot {10}^{27}{m}^{-3}}{\mathrm{one}+\mathrm{1,349}\cdot {10}^{27}{m}^{-3}{\left(\frac{\mathrm{0,089}-\mathrm{0,072}}{\mathrm{2,236}\cdot {10}^{-3}}\right)}^{\frac{\mathrm{one}}{0.5}}\mathrm{5,005}\cdot {10}^{27}\frac{m^3}{c}}=\mathrm{3,013}\cdot {10}^{24}{m}^{-3}\left(8\right)$$

$$d=2nm\cdot 3^{\frac{\ln \left(\mathrm{one}+\mathrm{5,005}\cdot {10}^{-27}\frac{m^3}{c}\cdot \mathrm{1,349}\cdot {10}^{27}{m}^{-3}{\left(\frac{\mathrm{0,089}-\mathrm{0,072}}{\mathrm{2,236}}\right)}^{\frac{\mathrm{one}}{0.5}}\right)}{\ln \left(13\right)}}=27nm\left(9\right)$$

On Fig presents the surface morphology of the film obtained using an atomic force microscope (AFM) from sols with different sizes of nanoparticles, the initial concentration of nanoparticles in the sol (C ₀ = 1,349 · 10 mρ). An orthosilicic acid sol was applied to a silicon (Si) substrate using a centrifuge using a metering device at a centrifuge speed of 3000 rpm for 2 minutes. Annealing was carried out at a temperature of 600 ° C for 30 minutes in air. Table 1 shows the values of the transmittance of infrared radiation through a sol of orthosilicic acid used for the manufacture of films (Fig. 14), as well as the average size of the nanoparticles determined by the ratio (2), (3), (4).

Table 1 T, rel. units d (T), nm Surface morphology 0.171 117 Figa 0.239 183 Figb 0.297 236 Figv 0.366 297 Fig.14g

The average size of the nanoparticles, determined by the present method, corresponds to the average size of the nanoparticles, determined by the AFM image of the surface morphology of the films (Fig. 14).

The inventive method can find application in the creation and production of nanostructured films from film-forming sols for gas-sensitive sensors.

Sources of information taken into account

1. RF patent No. 2393458, IPC G01N 15/02, G01N 21/00 Method for determining the average size of aggregates of filler particles, their concentration and distribution in the volume of the polymer matrix / Malanin M.N., Pakhomov P.M., Khizhnyak S.D. . // Bull. No. 18 dated 06/27/2010

2. Zhabrev V.A., Moshnikov V.A., Tairov Yu.M., Shilova O.A. Sol-gel - technology: textbook. allowance. SPb .: Publishing house of SPbGETU "LETI", 2004. - 156 p.

3. Averin I.A., Karpova S.S., Nikulin A.S., Moshnikov V.A., Pecherskaya P.M., Pronin I.A. Guided synthesis of thin glassy films // Nano- and microsystem technology. - 2011. - No. 1. - S.23-25;

Claims (1)

A method for determining the concentration and average size of nanoparticles in ash, which consists in the manufacture of reference samples with a given initial concentration of nanoparticles, recording infrared spectra of reference samples, identifying characteristic absorption peaks, characterized in that the infrared spectra of the reference samples are recorded during the coagulation process, the experimental dependence of the coefficient is built transmitting infrared radiation from the time of coagulation, record the infrared spectra of the samples and determine the concentration C and the size of the nanoparticles d according to the ratios
$$C\left(T\right)=\frac{C_0}{\mathrm{one}+C_0\tau \left(T\right)K},$$

$$d\left(T\right)=\alpha {\chi }^{\frac{\ln \left(\mathrm{one}+K\cdot C_0\cdot \tau \left(T\right)\right)}{\ln \left(\xi \right)}},$$

$$C_0=\frac{{\rho }_{\mathrm{to}}{V}_{\mathrm{to}}{N}_A}{M_{\mathrm{to}}{V}_{s\mathrm{about}l\mathrm{I\; am}}},$$

$$K=\frac{\mathrm{four}kT}{3\eta }\psi ,$$

where C ₀ is the initial concentration of nanoparticles in the ash;
K is the coagulation constant determined by the composition of the sol;
ρ _to is the density of the sol component forming the nanoparticles;
V _to is the volume of the sol component forming the nanoparticles;
N _A is the Avogadro number;
M _to - the molar mass of the sol component forming the nanoparticles;
V _sol - the volume of the sol;
k is the Boltzmann constant;
T = 298 K - temperature;
η is the dynamic viscosity of the solution;
ψ = 10 ^-9 is a parameter characterizing the effective probability of collision of nanoparticles with each other;
α is the size of the molecule forming the nanoparticle;
χ = 3 is the coefficient of growth of the diameter of the nanoparticles during coagulation;
ξ = 13 is a constant associated with the fractality of the nanoparticle;
τ (T) is an approximation of the experimental time dependence of the transmittance of infrared radiation through a sol.

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