JPH0785052B2 - Particle size distribution analysis method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of use] The present invention measures the intensity distribution of diffracted light or scattered light generated by irradiating dispersed sample particles with light using a plurality of detectors, and measures the measured intensity distribution. The present invention relates to a particle size distribution analysis method for obtaining the particle size distribution of sample particles from the above data.

[Conventional technology]

In the particle size distribution measuring device using the diffraction of light by particles or scattering phenomenon, the intensity distribution of diffracted light or scattered light, that is, the diffraction angle or the relationship between the scattering angle and the light intensity is measured,
The particle size distribution of the sample particles is calculated by performing arithmetic processing based on the Fraunhofer diffraction or Mie scattering theory.

FIG. 1 is a diagram schematically showing a measuring optical system of a general particle size distribution measuring device.

In FIG. 1, a sample cell 1 is a transparent container containing a medium containing dispersed sample particles, and the sample cell 1 is irradiated with parallel single-wavelength light L from a light source 2.

Around the sample cell 1, there are arranged a plurality of detectors d1, d2, ... dm for individually receiving the single wavelength light L diffracted or scattered by the sample particles in the sample cell 1 at each scattering angle. The particle size distribution of the sample particles can be obtained by subjecting the data of the light intensities g1, g2, ... Gm detected by these detectors d1, d2, ... Dm to arithmetic processing based on Fraunhofer diffraction or Mie scattering theory.

FIG. 2 shows the particle size distribution f ₀ (j) of the sample particles and the sensitivity curves p ₁ (j), p ₂ (j), ... P of the detectors d1, d2 ,.
₃ is a graph showing _m (j), where the horizontal axis represents the grain size j, the left vertical axis represents the sensitivity of the detectors d1, d2, ... dm, and the right vertical axis represents the particle amount.

In the conventional particle size distribution analysis method, the above arithmetic processing is performed as follows.

Now, the light intensity g1, g detected by each detector d1, d2, ... dm
2, ... Gm is a matrix G, and distribution sensitivity curves p ₁ (j), p ₂ (j), ... P _m (j) of each detector d1, d2, ... dm (hereinafter referred to as a response function if necessary) Is represented by a matrix P, and the particle size distribution f ₀ (j) is represented by a matrix F, the following relational expression G = PF (1) holds between the matrices G, P, F.

Therefore, in the conventional particle size distribution analysis method, the inverse matrix P ⁻¹ of the response function matrix P is first obtained, and from this and the relationship of the equation (1), F = P ⁻¹ G (2) Particle size distribution f ₀ (j)
Was required.

[Problems to be Solved by the Invention]

However, in the conventional particle size distribution analysis method described above,
Generally, the solution of the matrix F of the particle size distribution is likely to vibrate or diverge, and in order to avoid this, the number of detectors d1, d2, ... dm and the number of representative particle diameters are set equal, or the distribution of particle size distribution is There has been a problem that a matrix for defining the convergence condition for the shape and its curve has to be added separately, which makes the calculation process complicated.

In view of the above conventional drawbacks, the present invention provides a particle size distribution analysis method capable of obtaining a particle size distribution at arbitrary particle size intervals without vibrating or diverging the solution of the particle size distribution, and without depending on the number of detectors. It is intended to be provided.

[Means for Solving the Problems]

In order to achieve the above-mentioned object, the present invention measures the intensity distribution of diffracted light or diffused light generated by irradiating light on dispersed sample particles with a plurality of detectors, and from the measured intensity distribution data, the Fraunhofer In the particle size distribution analysis method for obtaining the particle size distribution of the sample particles based on the diffraction or Mie scattering theory, the assumed particle size distribution is set in advance, and the assumed particle size corresponding to the particle size range carried by each detector with the sensitivity of each detector as a weight. Calculate the calculated light intensity by each detector from each value of the distribution, the value in each particle size range in the assumed particle size distribution by the value according to the ratio of the difference between the calculated light intensity and the measured light intensity, respectively. Corrected, the corrected particle size distribution is used as a new assumed particle size distribution, and the same processing as above is sequentially repeated to calculate the calculated light intensity and the measured light intensity. Ratio of differences is characterized in that assuming particle size distribution of the true particle size distribution of when it becomes within a predetermined value.

[Action]

According to the above configuration, with the sensitivity of each detector as a weight, the calculated light intensity by each detector obtained from each value of the assumed particle size distribution corresponding to the particle size range carried by each disk, and the actually measured light intensity The assumed particle size distribution is converged to the true particle size distribution by correcting each value of the assumed particle size distribution corresponding to the particle size range carried by each detector according to the ratio of the difference, and repeating the correction process.

〔Example〕

An embodiment of the present invention will be described below with reference to an optical system of a general particle size distribution measuring device shown in FIG. 1 and a graph shown in FIG.

According to the particle size distribution analysis method of this embodiment, the distribution sensitivity curves of the detectors d1, d2, ... Dm, that is, the response functions p ₁ (j), p ₂ (j), ... p _m (j)
From the Fraunhofer diffraction or Mie scattering theory.

Then, when the substantial analysis is started, first, the assumed particle size distribution f (j) is determined. The variable j in this case represents the representative grain size. The assumed particle size distribution f (j) is, for example, secondly, as shown by the broken line, a uniform value α over the entire particle size range.
The particle size distribution can be set.

Next, for example, the above assumed particle size distribution f detected by the detector d1 associated with the particle size range R1 having the largest scattering angle
The calculated light intensity g'1 in (j) is obtained. The calculated light intensity g'1 is obtained from the assumed particle size distribution f (j) using the response function p ₁ (j) of the detector d ₁ as a weight. That is, g′1 = ∫p ₁ (j) · f (j) dj (1) is calculated.

Next, the ratio r ₀ between the light intensity g1 measured by the detector d1 and the calculated light intensity g′1 is r ₀ = g1 / g ′ ₁ = g1 / ∫p ₁ (j) · f ( j) dj ... Obtained from the equation (2).

With the value r ₀ of the ratio as a weight, the value of the assumed particle size distribution f ₁ (j) corresponding to the detector d ₁ is expressed by the following expression f ₁ (j) = {1+ (r ₀ −1) p ₁ (i)} f (J) ...
Correct as in (3).

Similarly, for the detector adjacent to the detector d1, that is, for the detector d2 associated with the grain size range R2 having the next largest scattering angle, the ratio r ₁ between the actually measured light intensity g2 and the calculated light intensity g′2. Ask for.

That is, the calculated light intensity g′2 in this case is obtained as g′2 = ∫p ₂ (j) · f ₁ (j) dj (4), and the ratio r ₁ is r ₁ = g2 / g ′ 2 = g2 / ∫p ₂ (j) · f ₁ (j) dj… (5)

Then, with the value r ₁ of the ratio as a weight, the value of the particle size distribution f ₂ (j) is calculated by the detector d ₂ as follows: f ₂ (j) = {1+ (r ₁ −1) p ₂ (j)} f ₁ ( j) ...
Correct as in (6).

Particle size distribution f corresponding to each of the following detectors d3, d4, ... dm
_{3 (j), f 4 (} j) ... Similarly sequentially corrected f _m (j).

Next, returning to the first detector d1, the second particle size distribution correction is performed.

Light intensity g of the calculation in this case _{'2 1, g' 2 1 = ∫p 1} (j) · f 1, obtained as m (j) dj ... (7 ). However, f _{1, m} (j) is the particle size distribution f _m (j) corresponding to the detector dm obtained in the first correction,
The subscript 1 represents the first correction. The subscript 2 of g ′ ₂ 1 also indicates that it is the second calculation result.

The value r _{2, 0} of the ratio in this case, from the equation _{r 2,0 = g1 / g '2} 1 = g1 / ∫p 1 (j) · f 1, m (j) dj ... (8) Ask. However, the subscript 2 of the ratio value r _2,0 represents the second calculation result.

Then, using the value r _2,0 of the ratio as a weight, the detector d1
The second corrected particle size distribution f _2,0 (j) of the particle size distribution f ₁ (j) corresponding to the following formula f _2,1 (j) = {1+ (r _2,0 −1) p ₁ (j )} F
Calculated from _{1, m} (j) (9).

The second corrected particle size distribution value f _2.2 (j) by the detector d2 is the ratio value r _2,1 r _2,1 = g2 / g ' ₂ 2 = g2 / ∫p ₂ (j) · f as _{2,1 (j) dj ... (10} ), the following equation _{f 2,2 (j) = {1+} (r 2,1 -1) p 2 (j)} f
_{Calculated from 2,1} (j) (11).

Similarly, the particle size distribution value f _2,1 (j) corrected by the i-th detector di for the second time is expressed by the following equation f _2,1 (j) = {1+ (r _2,1-1 −1). ) P _i (j)} × f _{2, i−1} (j) (12)

By repeating such correction in accordance with the arrangement order of the respective detectors d1, d2, ...
As the particle size distribution value f _{n, i} (j) corrected by the i-th detector di at the time, the following expression f _{n, i} (j) = {1+ (r _{h, i−1} −1) p _i (j)} × f _{n, i−1} (j) (13) can be obtained.

Further, the value r _{n, i−1} of the above ratio is expressed by the following equation r _{n, i−1} = gj / g ′ _n i = gi / ∫p _i (j) · f _{n, i−1} (j) dj. (14) can be obtained as

However, when the subscript (i-1) is 1, that is, the detector d1
When the particle size distribution value f _{n, i} (j) corrected by the above is obtained, as the particle size distribution correction value f _{n, i−1} (j) of the next adjacent detector used for that, one time before the detector dm,
That is, the (n−1) th correction value f _{n, i−m} (j) is adopted.

Then, | r _{n, i−1} −1 in each detector d1, d2, ... dm
When all of | are less than or equal to a predetermined fixed value, that is, when it can be considered that the assumed correction of the particle size distribution has proceeded sufficiently and converged to the true particle size distribution value, the above correction is terminated and Corrected particle size distribution value f
_{Let n, 1} (j) be the true particle size distribution value to be determined.

〔The invention's effect〕

The present invention is configured as described above, and the sensitivity of each detector is used as a weight, and the calculated light intensity by each detector is obtained from each value of the assumed particle size distribution corresponding to the particle size range carried by each detector, and the calculated light intensity is calculated. The assumed particle size distribution is corrected by correcting each value of the assumed particle size distribution corresponding to the particle size range of each detector according to the ratio of the difference between the light intensity and the actually measured light intensity, and repeating the correction process. Since the calculation solution of the particle size distribution does not oscillate or diverge, the particle size distribution can be obtained at an arbitrary particle size interval regardless of the number of detectors.

[Brief description of drawings]

1 and 2 are explanatory views of one embodiment of the present invention, FIG. 1 is a diagram schematically showing a measuring optical system of a general particle size distribution measuring device, and FIG. 2 is a particle size of sample particles. It is a graph which shows distribution and a sensitivity curve of each detector in the above-mentioned particle size distribution measuring device. d1 to dm …… detector, g1 to gm …… measured light intensity, f
(J) ...... assumed particle size _{distribution, p 1 (j) ~p m} (j) sensitivity ...... detectors share size range of R1 to Rm ...... detector.

Claims (1)

[Claims] 1. The intensity distribution of diffracted light or scattered light generated by irradiating dispersed sample particles with light is measured with a plurality of detectors, and based on Fraunhofer diffraction or Mie scattering theory based on the measured intensity distribution data. In the particle size distribution analysis method for obtaining the particle size distribution of the sample particles, an assumed particle size distribution is set in advance, and the detector is selected from the respective values of the assumed particle size distribution corresponding to the particle size range carried by each detector with the sensitivity of each detector as a weight. Calculate the calculated light intensity, correct the value in each particle size range in the assumed particle size distribution by a value corresponding to the ratio of the difference between the calculated light intensity and the measured light intensity, and then correct the particle size distribution. As a new assumed particle size distribution, the same processing as the above is sequentially repeated, and the difference between the calculated light intensity and the measured light intensity is within a predetermined value. The particle size distribution analysis method characterized by the assumptions particle size distribution and the true particle size distribution when the Tsu.