JPH0820355B2 - Particle size measurement method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention relates to the particle size of powders of alumina, silicon nitride, silicon carbide and the like used as raw materials for ceramic products,
The present invention relates to a method for measuring the particle size of powder such as silica sand and white alundum.

[Problems to be Solved by Conventional Techniques and Inventions] In a particle size measuring method using light transmission, it is necessary to know the transmittance and the extinction coefficient. Study of Rose (Ros
e, H, E., ″ The Measurement of Particle Size in Vevy
Fine Powders ″ Constable & Co. Ltd., London (195
There are many studies on the measurement of extinction coefficient, including 4), but the wavelength of transmitted light is not actively changed. In particular, there is no definite method for measuring the particle size characteristics of particles in the submicron range, which makes it difficult to understand the powder characteristics.

The recent submicron particle size measurement using light includes a light diffraction method, a light scattering method, a photon correlation method and the like, but it cannot be said to be simple and there are still various problems in measurement.

In other words, the optical diffraction method can measure a few μm to 200 μm
The representative particle size and distribution index are determined by the curve fitting method with the particle size distribution function, but the multiple diffraction phenomenon occurs depending on the concentration, and the apparent particle size is small. was there.

The measured particle size range by the light scattering method is 0.1 μm to several μm, and the particle parameter α is defined as α = πD / λ (where λ is the light source wavelength and D is the particle size). Since the incident light wavelength must be shortened when measuring particles, a He—Cd laser or a He—Ne laser light source is required, and errors due to the angle dependence of the light scattering phenomenon occur, which is also expensive. In addition, since there is temperature dependence, an error will occur unless the temperature is controlled.

In the photon correlation method, since the counting process is performed on the assumption that the particle size distribution is Gaussian distribution, the error is large for particles that do not have Gaussian distribution. In addition, the measuring device is expensive.

Regarding the particle size measurement of monodisperse particles, the method of Heller et al. (Pangonis, WJ, Heller, S., and Econ, which does not depend on particle concentration, is used.
omou, NA, J.Chem.Phys., 34,960 (1961) and Gucker's method (Gucker, FT, and Rowell, RL, Disc.Frad.Soc., 3
0,185 (1960)), but it is not practical in terms of equipment and conditions.

In addition, the method of measuring the particle size by particle concentration is Hell
er et al. (Heller, W., and Nakagaki, M., J.chem.Phy
s., 31,1188 (1959)), Inn et al.'s method (La Mer.VK, In
n, ECY, and Wilson, IB, J.Colloid Sci., 18,888 (1
963)) and the method of Hots et al., Which evaluates the particle size by taking the maximum value of the Tyndall phenomenon, but there is a problem in the calculation of the extinction coefficient.

In view of this, an object of the present invention is to provide a method which is inexpensive and enables accurate particle size measurement by a simple operation.

[Means for Solving the Problems] The particle size measuring method according to the present invention is a light scattering phenomenon in which the particle size of particles in the submicron region having a particle size of 0.1 to 1 μm is measured using light having a specific wavelength of 200 to 1100 nm. In the method for measuring the particle size in the region in which the particle size is generated, the transmittance (T) of the dispersion liquid of the powder for a reference powder having a known particle size is measured to obtain the dispersion liquid concentration (c [g / cm ³ ]) Is the formula (a) below
ie, the dispersion liquid of a plurality of reference powders having known particle diameters is determined by determining the concentration of the specific dispersion liquid of the reference powder within a concentration range satisfying the deviation from the theory within 1%. With respect to the specific wavelength, the relationship between the particle size (D) and the extinction coefficient (K) was approximated by a straight line represented by the following formula (B), and this formula (B) and Lambert-Beer's The empirical formula shown in the following formula (C), which represents the relationship between the transmittance (T) of the dispersion liquid and the powder particle size (D), is calculated in advance, and the above-mentioned specification is made for the dispersion liquid of the particle size measurement target powder. The transmittance of wavelength light is measured, and the particle size is calculated from the above empirical formula.

Formula (a); logT = a · c (where T = transmitted light intensity / incident light intensity, a
= Constant. ) Equation (b); logK = α _i logD + β _i (where α _i and β _i = constant, i = 1,2.) Equation (c); D = EXP {(β _i −logZ) / (1- α _i )} (where Z = −ρlogT / 1.5cl, ρ = particle density, 1 = optical path length in the dispersion liquid) where the particle size (D) and the extinction coefficient (K) The relationship is approximated to the following equation (d), and this equation (d) and Lambert-Bee
The transmittance (T) shown in the following equation (e) by the equation of r
The empirical formula representing the relationship between the particle size and the powder particle size (D) may be obtained.

Formula (d); K = mD ³ (where m = constant) (Where, Z = −ρlogT / 1.5cl, ρ = particle density, 1 = optical path length in the dispersion liquid.) Further, for the dispersion liquid of the particle size measurement target, the dispersion liquid of the powder is specified. The transmittance (T) for the wavelength light is measured, and the dispersion liquid concentration (c [g / cm ³ ]) is calculated according to the above formula (a) by Mie.
Within the concentration range where the deviation from theory is within 1%,
The specific dispersion liquid concentration of the particle size measurement target powder is determined, and the transmittance of the specific wavelength light is measured for the dispersion liquid of the particle size measurement target powder prepared to have the specific dispersion liquid concentration, and the experiment is performed. It is desirable to calculate the particle size from the formula.

Furthermore, it is desirable to use long wavelength light of 800 nm or longer.

[Operation] In the particle size measuring method of the present invention, particle size measurement in a region where a light scattering phenomenon occurs, in which the particle size of particles in the submicron range of 0.1 to 1 μm is measured using light of a specific wavelength of 200 to 1100 nm. In determining the empirical formula showing the relationship between the transmittance of the dispersion liquid and the particle size, the transmittance (T) of the dispersion liquid with respect to the specific wavelength light is first determined for the reference powder having a known particle size. Whether or not (c) satisfies expression (a) within a range of deviation from Mie theory of 1% or less, that is, logT-
The linearity of the c-curve is confirmed, and the specific dispersion liquid concentration is determined within the concentration range that satisfies such conditions. Therefore, the specific dispersion liquid concentration of the reference powder having a known particle diameter is set within a range that does not cause multiple scattering with respect to the specific wavelength light, and therefore, in the subsequent step of obtaining the empirical formula, the Lambert-Beer formula is used. Can be applied. Also, by a simple method of confirming this linearity, it is easy to increase the sensitivity of measurement of transmittance in the step of obtaining the empirical formula by setting the concentration of the specific dispersion as high as possible within the range where multiple scattering does not occur. Is. If the deviation from the Mie theory is larger than 1%, high measurement accuracy cannot be obtained due to multiple scattering.

Then, as described above, when the transmittance of the specific wavelength light is measured using the reference powder dispersion liquid having a plurality of known particle diameters adjusted to the specific dispersion liquid concentration, the formula ( The linear approximation formula with small error shown in) is established.

As a result, in the submicron region where a good empirical formula has not been obtained conventionally, a highly accurate and simple empirical formula represented by the formula (C) between the particle diameter and the absorption coefficient can be obtained.

Then, by using this empirical formula, the particle size is measured for the dispersion liquid of the particle size measuring symmetrical powder, and the particle size is calculated by measuring the transmittance of the specific wavelength light, so that the particle size can be obtained easily and with high accuracy. it can.

In the above, if the relationship between the particle size (D) and the extinction coefficient (K) is approximated to the expression (D), the expression (E) indicating the relationship between the transmittance (T) and the particle size (D) is obtained. This simplifies the particle size measurement, and thus enables simpler particle size measurement.

Further, if the dispersion and the concentration of the powder of the particle size measurement object are adjusted so that the transmittance and the concentration satisfy the equation (a) within the range of 1% from the Mie theory, the concentration is adjusted. Since the dispersion liquid of the particle diameter measurement target powder used when calculating the particle diameter from the above empirical formula does not cause multiple scattering, the measurement error of the transmittance of the dispersion liquid is small. Therefore, the measurement error of the particle size is small.

Further, at this time, in order to increase the measurement sensitivity of the transmittance of the powder dispersion for particle size measurement, it is easy to set the concentration of the specific dispersion as high as possible within the concentration range where multiple scattering does not occur.

In the above, if long-wavelength light of 800 nm or more is used, the linearity between the extinction coefficient and the particle size becomes better, and especially equation (d) becomes better, and its accuracy is improved. Will be very good. Further, the longer the wavelength of light, the higher the concentration of the dispersion liquid, the equation (a) holds,
It is easy to increase the measurement sensitivity.

[Example] FIG. 1 is an optical system diagram of a spectrophotometer which is preferably used in a particle size measuring method according to an example of the present invention.

This spectrophotometer is equipped with a deuterium lamp D ₂ and a halogen lamp.
It is an ultraviolet-visible spectrophotometer having a measurement wavelength range of 200 nm to 1100 nm and having two light sources of WI. The light emitted from the light source D ₂ or WI passes through the window plate W, is reflected by the light source condensing mirror M ₁ , and then enters the diffraction grating G through the entrance slit S ₁ . The light diffracted by the grating G and exiting the exit slit S ₂ passes through the stray light cut filter F, enters the mirror M _2, and is split by the half mirror M ₃ into a sample-side light beam and a control-side light beam. After being reflected again at ₄ and M ₅ , they enter the sample chamber through the window plate W respectively. In the sample chamber, the sample cell Sam. And the control cell Ref.
The light fluxes that have respectively passed through and are condensed by the lens L and then enter the photodiode PD which is a photodetector.

When using this spectrophotometer, the powder dispersion is set as the sample side cell Sam., While only the dispersion medium is set as the control side cell Ref. At this time, it is possible to measure the attenuation ratio of the transmitted light, that is, the transmittance, when the powder particles are present as compared to when the powder particles are not present.

Also, using this spectrophotometer, data regarding light transmission with single wavelength light is obtained for a dispersion liquid of a powder having a known particle diameter, the dispersion liquid concentration of which is within a range where multiple scattering does not occur.

In general, the Lambert-Beer law of a monodisperse system that holds in a dilute concentration range where multiple scattering does not occur is represented by the following equation (1).

log (I ₀ / I) = KAcl (1) I ₀ : incident light intensity, I: transmitted light intensity, K: extinction coefficient, A: particle projected area (in 1g light flux), c: particle weight concentration, l: Optical path length in the dispersion.

Here, since the transmittance T = I / I ₀ , the equation (1) becomes the following equation (9).

logT = KAlc (9) If the transmittance T of a powder dispersion having a known particle size is measured, the extinction coefficient K can be obtained from the equation (9).

As the powder used for data collection, for example, silica (SiO ₂ ) particles which are monodisperse spherical particles and polystyrene latex particles can be used. Here, the results of polystyrene latex particles are shown in FIG. Polystyrene latex particles are 0.061μm ~ 1.696μ
Use a particle size of m (11 types).

Extinction coefficient (K) -particle size (D) drawn on a log-log graph
The curve shows a tendency that as the particle size (D) increases, the absorption coefficient K increases and reaches a maximum value and then enters the vibration range. Under the condition of wavelength λ = 900 nm to 1100 nm, the absorption coefficient K is almost proportional to the cube of the particle size D. Also,
As the particle diameter D becomes smaller, it enters the vibration range to the attenuation range. At this time, in the region where the wavelength λ is long, the absorption coefficient K is attenuated linearly and parallel to each other for each wavelength.

In the attenuation region of the extinction coefficient K in the range of the particle size of 0.1 μm to 1.0 μm shown in FIG. 2, the relationship between the extinction coefficient K and the particle size D can be approximated by two straight lines. That is, the extinction coefficient K can be expressed by the equation (2) using the constants α _i and β _i .

logK = α _i logD + β _i (2) (i = 1,2) On the other hand, from Lambert-Beer's law (equation (1)), log (I ₀ /I)=1.5 Kcl / ρD (3) Here, ρ: particle density, D: particle size.

The particles are spherical, and the following empirical formula (4) is obtained from the formulas (2) and (3).

D = EXP {(β _i −logZ) / (1−α _i )} (4) Here, Z is Z = ρlog (I ₀ /I)/1.5cl (5).

Since I ₀ / I = 1 / T in formula (5), formula (4) is an empirical formula showing the relationship between the transmittance T and the particle size D.

Next, of the data in FIG. 2, only the data with the wavelength λ = 1100 nm, which has the best linearity, is extracted and shown in FIG.

As shown in FIG. 3, if it is approximated that the extinction coefficient K is proportional to the cube of the particle diameter D in the attenuation region of the polystyrene latex particle diameter of 0.1 μm to 1.0 μm, the extinction coefficient K is calculated using the constant m. Can be expressed by equation (6).

K = mD ³ (6) By substituting this equation (6) into the Lambert-Beer equation and considering that the constant m is almost equal to 1 in the case of polystyrene latex particles, log (I ₀ /I)=1.5 clD ² / ρ (7) Here, the following equation (8) is obtained.

Since I ₀ / I = 1 / T in the formula (5), the formula (8) is an empirical formula showing the relationship between the transmittance T and the particle diameter D.

After creating an empirical formula representing the relationship between the transmittance T and the particle size D for a dispersion liquid of powder having a known particle size as described above,
The following particle size measurement operation is performed.

First, the measured powder to be measured for particle diameter is charged into a fixed amount of water, and the charged powder is dispersed in water by ultrasonic dispersion and manual stirring to prepare a uniform stock solution of known concentration. The stock solution is diluted to prepare samples of four kinds of concentrations, for example. As shown in FIG. 4, cells 1 to 4 have, for example, 20% and 40%.
Prefill water up to the%, 60% and 80% marked lines respectively. Then, the above stock solution is poured into each cell to make the liquid amount in each cell 100%, and ultrasonic dispersion and manual stirring are further performed. The water used as the dispersion medium is preferably deionized water with an ion exchange resin. However, the dispersion medium is not limited to water, and can be appropriately changed according to the type of powder. A dispersant such as sodium hexametaphosphate may be used if necessary.

Cells 1 to 4 are sequentially set in the spectrophotometer as sample side cells Sam. A light source having a wavelength of 1100 nm, for example, is selected, and the light transmittance T of the photodiode PD is measured.

A high particle concentration is desirable in order to increase the sensitivity of particle size measurement. That is, if the particles are too thin, the measured concentration will deteriorate. On the contrary, even if the particle concentration is too high, multiple scattering occurs and an error occurs. Therefore, while confirming that multiple scattering does not occur through the graph of transmittance (logT) -particle weight concentration (c) showing linearity, the particle concentration should be as high as possible within the range not reaching the multiple scattering region. To do.

The measurement error can be minimized by increasing the concentration of the dispersion liquid of the particle size measurement target powder within the range where multiple scattering does not occur.

FIG. 5 is a diagram showing the relationship between the transmittance T and the particle weight concentration c for submicron particles of polystyrene latex (particle diameter D = 0.061 μm). FIG. 6 and FIG. 7 are similar views when the particle size of the same particles is D = 0.208 μm and D = 0.309 μm, respectively. Draw a graph of transmittance-concentration similar to these three figures and keep the deviation from Mie theory within 1%.

Even when the dispersion concentration of the reference powder is adjusted to a range that does not cause multiple scattering, a transmittance-concentration graph is drawn in the same manner so that the dispersion exhibits linearity.

By setting the dispersion concentration of the reference powder as high as possible within the range where multiple scattering does not occur, it is possible to determine an empirical formula that is well suited to the actual value.

If the transmittance T is obtained as described above, the particle diameter D can be calculated using the empirical formulas (4) and (8). Since the empirical formula in the submicron range does not hold in the range where the particle size D exceeds 1 μm, when the particle size calculation results of the formulas (4) and (8) exceed 1 μm, an appropriate method is used. Use the calculated particle size in the micron range.

As described above, according to the present invention, the particle size in the submicron range of 0.1 μm to 1.0 μm can be easily measured by the present invention. Further, the relationship between the transmittance of the dispersion liquid and the particle size of the powder has generality and commonality among various powder particles.

Further, since the particle size distribution width of submicron particles is sharp, the present invention can be applied to perform particle size measurement with particularly high accuracy. However, the method of the present invention can be applied even when particles having different particle sizes are mixed.

[Effects of the Invention] As described above, the inventor of the present invention determines the concentration of the dispersion liquid of the reference powder when determining the empirical formula showing the relationship between the transmittance and the particle size of the dispersion liquid in the measurement of the particle size in the submicron range. It was found that the absorption coefficient of the dispersion shows linearity with respect to the particle diameter when the is prepared within the range where multiple scattering does not occur. In the particle size measuring method of the present invention, since the empirical formula is obtained by utilizing this linearity, a simple and precise empirical formula can be obtained, and therefore the accuracy of the particle size calculated from the empirical formula is high.

As described above, conventionally, it was common knowledge that the particle size in the submicron range of 0.1 μm to 1.0 μm could be measured only by using the short-wavelength light. It is possible to provide a method in which the diameter can be easily measured even with long-wavelength light, and the particle size can be accurately measured at a low cost by a simple operation.

According to the present invention, the value of the particle diameter obtained is the diameter of a circle having an area corresponding to the projected area of the background when the powder particles are exposed to light, so that the particle shape is always This projected area diameter can be obtained.

[Brief description of drawings]

FIG. 1 is an optical system diagram of a spectrophotometer used in a particle size measuring method according to an embodiment of the present invention, and FIG. 2 is a diagram showing a relationship between an extinction coefficient K of polystyrene latex particles and a particle size D. , Fig. 3 is a diagram showing a case where the wavelength λ = 1100 nm is extracted from the data in Fig. 3, and Fig. 4 is a sample side cell in the spectrophotometer of Fig. 1 for particle size measurement. FIG. 5 is a process diagram showing a process of producing cells of four kinds of concentrations to be set, FIG. 5 is a diagram showing the relationship between the transmittance T and the particle weight concentration c for submicron particles of polystyrene latex, and FIG. FIG. 7 is a view similar to the previous figure of polystyrene latex submicron particles of other particle sizes, and FIG. 7 is a view similar to FIG. 5 of polystyrene latex submicron particles of other particle sizes. Explanation of symbols D ₂ …… Deuterium lamp, F …… Filter G …… Diffraction grating, L …… Lens M _{1 to} M ₅ …… Mirror, PD …… Photodiode Ref. …… Control side cell, Sam …… Sample side cell S ₁ , S ₂ …… Slit, W …… Window plate WI …… Halogen lamp D …… Particle size K …… Extinction coefficient T …… Transmittance

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Mitsukuni Mizuno 3-5-12 Yoshino, Higashi-ku, Nagoya, Aichi Prefecture (72) Inventor Shoji Yabuuchi 2-20-1, Shinmori, Asahi-ku, Osaka-shi, Osaka ( 56) References JP 59-159051 (JP, A) JP 55-131749 (JP, A) JP 62-175644 (JP, A) JP 60-158337 (JP, A) Sho 63-118549 (JP, U) “Powder Engineering Research Group,” Particle Size Measurement Technology, P. 164, Nikkan Kogyo Shimbun (Published August 20, 1975)

Claims (5)

[Claims] 1. The particle size of particles in the submicron region having a particle size of 0.1 to 1 μm is measured using light having a specific wavelength of 200 to 1100 nm,
In a particle size measuring method in a region where a light scattering phenomenon occurs, the transmittance (T) of a dispersion liquid of this powder with respect to a specific wavelength light is measured for a reference powder having a known particle size to obtain a dispersion liquid concentration (c [g / cm ³ ]) determines the specific dispersion liquid concentration of the reference powder within a concentration range in which the deviation from the Mie theory satisfies the following formula (a) within 1% and is adjusted to the specific dispersion liquid concentration. With respect to the dispersion liquid of the plurality of reference powders having known particle diameters, the transmittance of the specific wavelength light was measured, and the relationship between the particle diameter (D) and the extinction coefficient (K) was calculated by the following formula (B).
Approximate with the straight line shown in, and the empirical formula shown in the following formula (C) that represents the relationship between the transmittance (T) of the dispersion liquid and the powder particle size (D) by this formula (B) and the Lambert-Beer formula The particle size measurement method is characterized in that the transmittance of the specific wavelength light is measured for the dispersion liquid of the particle size measurement target powder, and the particle size is calculated from the empirical formula. Formula (a); logT = a · c (where T = transmitted light intensity / incident light intensity, a
= Constant. ) Formula (b); logK = α _i logD + β _i (where α _i , β _i = constant, i = 1,2.) Formula (c); D = EXP {(β _i −logZ) / (1- α _i )} (where, Z = −ρlogT / 1.5cl, ρ = particle density, l = optical path length in the dispersion liquid.) 2. A particle size measuring method in a region in which a light scattering phenomenon occurs in which a particle size of submicron particles having a particle size of 0.1 to 1 μm is measured using light having a specific wavelength of 200 to 1100 nm. The dispersion liquid transmittance (T) and the powder particle diameter (D) shown in the following formula (C) used when calculating the particle diameter of this powder from the transmittance of the specific wavelength light measured for the body dispersion liquid
The empirical formula expressing the relationship with is calculated by measuring the transmittance (T) of a dispersion liquid of this powder with respect to light of a specific wavelength for a reference powder having a known particle size, and measuring the dispersion liquid concentration (c [g / cm ³ ] ) Determines the specific dispersion liquid concentration of the reference powder within a concentration range in which the deviation from the Mie theory satisfies the following formula (a) within 1%, and a plurality of known dispersion liquids prepared to have the specific dispersion liquid concentration are prepared. With respect to the dispersion liquid of the reference powder having a particle diameter, the transmittance of the specific wavelength light is measured, and the relationship between the particle diameter (D) and the extinction coefficient (K) is expressed by the following formula (B).
A method for measuring particle diameter, which is characterized by approximating with a straight line shown in, and obtaining by this formula (b) and the Lambert-Beer formula. Formula (a); logT = a · c (where T = transmitted light intensity / incident light intensity, a
= Constant. ) Formula (b); logK = α _i logD + β _i (where α _i , β _i = constant, i = 1,2.) Formula (c); D = EXP {(β _i −logZ) / (1- α _i )} (where, Z = −ρlogT / 1.5cl, ρ = particle density, l = optical path length in the dispersion liquid.) 3. The relationship between the particle diameter (D) and the extinction coefficient (K) is approximated to the following formula (d), and this formula (d) and Lambert-B
3. The empirical formula representing the relationship between the transmittance (T) and the powder particle size (D) shown in the following formula (e) is obtained from the equation of eer, and the empirical formula is obtained. Particle size measurement method. Formula (d); K = mD ³ (where m = constant) (Where Z = −ρlogT / 1.5cl, ρ = particle density, l = optical path length in the dispersion.) 4. A dispersion liquid of the powder to be measured for particle size,
The transmittance (T) of the dispersion liquid of this powder for light of a specific wavelength was measured, and the dispersion liquid concentration (c [g / cm ³ ]) was calculated by the above formula (a).
Within the concentration range where the deviation from the Mie theory is within 1%, the specific dispersion liquid concentration of the particle size measurement target powder is determined, and the particle size measurement target powder adjusted to this specific dispersion liquid concentration is determined. For the body dispersion, measuring the transmittance of the specific wavelength light,
The particle size measuring method according to claim 1, wherein the particle size is calculated from the empirical formula. 5. The particle size measuring method according to claim 1, wherein long-wavelength light of 800 nm or more is used.