JP2009145356A - Method for estimating particle shape in liquid - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for estimating a particle shape for clarifying not only a shape of a particle in liquid but also a size of a shape. <P>SOLUTION: A minimum value of a square of a difference between a graph which is graphed by substituting in a particle model equation and a graph which is graphed by relating a wavelength (λ) and a scattering angle (Θ) to intensity (Y) is obtained on all of the particle model equations. The shape and size of the particle can be estimated by selecting the minimum value from among them, and selecting the most approximate particle model equation to the graph which is graphed by substituting in a relational expression expressing the light intensity (Y) by the wavelength (λ) and the scattering angle (Θ) out of the graphs which graph the particle model equations. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a shape of particles dispersed in a liquid and a method for estimating the size of the shape.

  Conventionally, particles of objects to be measured such as proteins, polymer compounds, surfactant micelles, and other molecular aggregates dispersed in a liquid are about a nanometer in size. It was common to observe with a force microscope. In order to observe these particles with an electron microscope, first, a chemical treatment such as freezing and dehydrating a sample as an object to be measured in a liquid must be performed, and observation must be performed under vacuum. For this reason, the particle morphology may change during the chemical treatment, and the particle image observed with an electron microscope may be different from the particle morphology in the liquid. The atomic force microscope has an advantage that it can be observed not only in a vacuum but also in a liquid, but there is a limit to the size that can be observed.

  Therefore, a scattering method has been used in which a liquid is directly irradiated with an electromagnetic wave (neutron, X-ray, light) and measured. As a generally performed method of the scattering method, there is a Guinier method. This method takes the square of the scattering vector on the horizontal axis and the logarithm of the scattering intensity on the vertical axis, and in the region where the square of the scattering vector is small, between the square of the scattering vector and the logarithm of the scattering intensity, The decreasing proportional relationship is established. Extrapolating this proportional line yields the origin scattering intensity, and the molecular weight of the particle can be calculated from the origin scattering intensity. From the slope of this proportional line, the inertia indicating the approximate size of the particle The radius can be calculated.

Further, from the scattered X-ray spectrum obtained based on the small-angle X-ray scattering method, the horizontal axis is the square of the scattering vector k (k ² = (4πsinΘ / λ) ² ), and the vertical axis is the common logarithm of the intensity Y (Log _10). Y) is obtained as a standard spectrum f (k ² ), and further a straight line group Li (Log ₁₀ Yi = −αDik) having a slope (−αDi) corresponding to the particle diameter Di (where i = 1 to n is a natural number). ² i +
It is expressed as Log ₁₀ βi. ) From the y-intercept (Log ₁₀ βi) and the slope (−αDi) of the straight line group Li when the standard spectrum f (k ² ) is approximated by the composite spectrum g (k ² ) represented by the linear combination (ΣLi). There is known a particle size distribution measuring method for obtaining a particle content with respect to a predetermined particle diameter Di (for example, Patent Document 1).

JP2003-139680

  However, in the method described in Patent Document 1, since the predetermined particle diameter is obtained on the assumption that the shape of the particles is spherical, the particles dispersed in the actual liquid are other than spherical. Since particles are also present, it was impossible to determine the size of the particles dispersed in the actual liquid and the size based on the shape.

  An object of the present invention is to provide a particle shape estimation method for clarifying not only the shape of particles in a liquid but also the size of the shape.

  A first aspect of the present invention is a particle shape estimation method for estimating the shape of particles dispersed in a liquid, a light irradiation step for irradiating light in particles in the liquid, and scattering scattered from the particles The scattered light detection step for detecting light, the storage step for storing the detection intensity (Y1) and the scattering angle (Θ) of each scattered light detected by the scattered light detection step for each scattered light, and the storage step. The scattering vector k (k = 4πsinΘ / λ, where π is the circular ratio) is calculated for each scattered light from the scattering angle (Θ) and the wavelength (λ) of the light irradiated to the particles by the light irradiation step, and the scattering vector (K) and the detected intensity (Y1) of the scattered light for each scattering angle (Θ) used for the calculation of the scattered vector (k), the detected intensity of the scattered light with the scattered vector (k) as the horizontal axis An experimental graph for obtaining an experimental graph with (Y) on the vertical axis A particle model expression expressing the intensity of the scattered light (Y) with the scattering vector (k) as a variable, and different particle model expressions depending on the shape of the particles are stored in advance in the storage means. The particle model formula selection step for selecting the particle model formula stored in the memory, and the particle model formula selection step, which is selected in the particle model formula selection step, is determined in advance as an unknown number of the particle model formula with the number related to the particle shape and the particle density as an unknown number. A particle model initial value setting step for setting the particle model formula by substituting the initial value, and a scattering calculated by the experimental graphing step to the particle model formula in which the initial value is substituted in the particle model formula initial value setting step Substituting the vector (k), the calculated intensity (Y2) of the scattered light is calculated, and the scattered vector (k) and the calculated intensity (Y2) of the scattered light are used. Particle model formula for obtaining a particle model formula setting graph with the scattering vector (k) on the horizontal axis and the intensity (Y) of scattered light on the vertical axis. The number related to the particle shape and particle density of the particle model formula is set so that the square of the difference between the graph and the particle model formula setting graph obtained by the graph modeling step is set to a minimum, and the set number is set. Graph difference square minimum value storing step for storing the number relating to particle shape and particle density, and the minimum square value of the difference between the experimental graph and the particle model equation setting graph, and selecting by the particle model equation selecting step The smallest value of the minimum squares of the differences between the experimental graph stored by the graph difference square minimum value storage step and the particle model formula setting graph for all the particle model formulas And a particle shape estimation step of estimating a particle shape from the particle model equation.

  According to the present invention, for all particle model formulas selected in the particle model formula selection step, the minimum value of the square of the difference between the experimental graph and the particle model formula setting graph is obtained, and the smallest of the minimum values is obtained. By selecting the value particle model equation, the particle shape can be estimated from the particle model equation.

A second aspect of the present invention is a particle shape estimation method for estimating the shape of particles dispersed in a liquid and the size of the shape, a light irradiation step of irradiating light on particles in the liquid; A scattered light detection step for detecting scattered light scattered from the particles, and a storage step for storing the detected intensity (Y1) and the scattering angle (Θ) of each scattered light detected by the scattered light detection step for each scattered light;
Scattering vector k (k = 4πsinΘ / λ, π is the pi) is calculated for each scattered light from the scattering angle (Θ) memorized by the memory step and the wavelength (λ) of the light irradiated to the particles by the light irradiation step. Then, using the scattering vector (k) and the detected intensity (Y1) of the scattered light for each scattering angle (Θ) used for the calculation of the scattering vector (k), the scattering vector (k) is plotted on the horizontal axis. Obtain an experimental graph with the scattered light intensity (Y) on the vertical axis. An experimental graphing step, and a particle model formula that expresses the scattered light intensity (Y) with the scattering vector (k) as a variable. Different particle model formulas are stored in advance in the storage means, a particle model formula selection step for selecting the particle model formula stored in the storage means, and a particle shape and a particle selected in the particle model formula selection step. Density of Substituting a predetermined initial value for the unknown number of the particle model formula with the number relating to the unknown as the unknown, setting the particle model formula initial value, and setting the initial value in the particle model formula initial value setting step By substituting the scattering vector (k) calculated in the experimental graphing step into the particle model equation, the calculated intensity (Y2) of the scattered light is calculated, and the scattered vector (k) and the calculated intensity of the scattered light ( Y2), a particle model equation setting graph for obtaining a particle model equation setting graph with the scattering vector (k) on the horizontal axis and the intensity (Y) of scattered light on the vertical axis is obtained in the setting graphing step and the experimental graphing step. The particle shape and particle shape of the particle model formula so that the square of the difference between the obtained experimental graph and the particle model formula setting graph obtained by the particle model formula setting graph step is minimized. A graph difference squared minimum value that stores a number relating to the density of the particle, a number relating to the set particle shape and particle density, and a minimum square value of the difference between the experimental graph and the particle model formula setting graph For all the particle model formulas selected by the storage step and the particle model formula selection step, the minimum square value of the difference between the experimental graph stored by the graph difference square minimum value storage step and the particle model formula setting graph is set. The particle model formula with the smallest value is selected, the shape of the particle is estimated from the particle model formula, and the particle size is calculated from the number related to the particle size of the particle model formula set by the graph difference square minimum value storing step. And a particle shape estimation step for estimating the size of.

  According to the present invention, for all particle model formulas selected in the particle model formula selection step, the minimum value of the square of the difference between the experimental graph and the particle model formula setting graph is obtained, and the smallest of the minimum values is obtained. By selecting a particle model equation of value, the shape of the particle can be estimated from the particle model equation, and the particle size can be estimated from the number related to the particle size of the particle model equation. Thereby, not only the shape of the particle | grains in a liquid but various sizes accompanying the shape of the particle | grain can be clarified.

In the third aspect of the present invention, in addition to the first or second aspect, the particle model equation initial value setting step is a particle model equation that is determined by the shape of the particles. Y = n × Δβ ² × V ² × P × S &#61472;&#61472; (where n is the number density of the particles, V is the volume of the particles, Δβ is the difference between the scattering length densities of the particles and the solvent, P is the particle shape factor (a function of the scattering vector k)) , S uses a structure factor (a function of the scattering vector k)).

  In the fourth aspect of the present invention, in addition to the first or second aspect, the experimental graphing step is based on the wavelength (λ) and scattering angle (Θ) of the light irradiated to the previously stored particles. A scattering vector k (k = 4π sin Θ / λ, where π is a pi) is calculated.

  According to the present invention, since the scattering angle (Θ) of the scattered light can be obtained in advance based on the detection position, when calculating the scattering vector k, the wavelength (λ) of the light irradiated on the previously stored particles and By using the scattering angle (Θ), the scattering vector k can be easily calculated.

  According to a fifth aspect of the present invention, in addition to the first or second aspect, the light irradiated into the liquid by the light irradiation step is X-rays or neutrons.

  According to the present invention, the shape of particles can be estimated even when irradiated with X-rays or neutrons.

  Hereinafter, an embodiment of a particle shape estimation method of the present invention will be described with reference to the drawings. FIG. 1 is a block diagram of a particle shape estimation apparatus used in a particle shape estimation method according to an embodiment of the present invention.

As shown in FIG. 1, the particle shape estimation apparatus 1 includes an X-ray generation source 2, a slit 3, a container 4, a vacuum path 5, a detector 6, and a computer unit 7.

  The X-ray generation source 2 generates X-rays and irradiates particles (measurement object) in a liquid with X-rays having a wavelength λ. In the present embodiment, the X-ray generation source 2 has been described as the light generation source. However, the present invention is not limited to this, as long as the scattering method can be used. Good.

  The slit 3 narrows the X-rays generated by the X-ray generation source 2 to a specific area. The X-rays narrowed by the slit 3 are contained in a liquid stored in a container 4 such as a quartz cell or a mica cell. The particles are irradiated. X-rays hitting the particles are scattered by the particles.

  The X-rays (scattered light) scattered by the particles pass through the vacuum path 5 and the intensity (Y1) of the scattered light is detected by the detector 6 at each scattering angle (Θ) at which the scattered light is emitted. Specifically, the detector 6 has a plurality (256 in the present embodiment) of scattered light detectors (not shown) for detecting scattered light, and the scattered light is detected by each scattered light detector. Intensity (Y1) and scattering angle (Θ) are detected. And the intensity | strength (Y1) of the scattered light detected for every scattering angle ((theta)) which scattered light is emitted by this detector 6 is each memorize | stored in the memory | storage means 8 of the computer part 7 mentioned later. Since this scattered light detector (not shown) is arranged at a specific position, the scattering angle (Θ) detected by the scattered light detector is a specific value for each scattered light detector. The scattering angle (Θ) for each light detection unit may be stored in advance in the storage unit 8 of the computer unit 7 to be described later, and the scattering angle (Θ) stored in the storage unit 8 may be used.

  Next, processing in the computer unit 7 will be described. The computer unit 7 includes a storage unit 8, an experiment graphing unit (experiment spectrum calculating unit) 9, a particle model formula selecting unit 10, a particle model formula initial value setting unit 11, and a particle model formula setting graphing unit (geometric). Academic spectrum calculation means) 12, graph difference square minimum value storage means 13, and particle shape estimation means 14.

  As described above, the storage unit 8 stores the light intensity (Y1) and the scattering angle (Θ) of the scattered light detected by the detector 6 for each scattered light, and a scattering vector k (k = 4πsinΘ / [lambda] and [pi] are also stored. The storage means 8 also stores the wavelength (λ) of X-rays generated from the X-ray generation source 2, and is a particle model formula (geometric model formula (formula 2 in formula 1) that is determined by the shape of the particles to be described later. (Expression substituted with Expression 19)) is also stored. In this embodiment, the particle model formula (geometric model formula (scattering formula)) determined by the wavelength (λ) of X-rays generated from the X-ray generation source 2 by the storage means 8 and the shape of the particles. However, the present invention is not limited to this, and the particle model formula (geometric model formula (scattering method) that is determined by the wavelength λ of the X-rays generated from the X-ray generation source 2 and the shape of the particles is stored in separate storage means. May be stored.

Ｙ２ ：散乱波（電磁波）の強度（散乱ベクトルｋ（４πｓｉｎΘ／λ）の関数）
ｎ ：粒子の数密度
Ｖ ：粒子の体積
Δβ：散乱長密度の差
Ｐ ：粒子形状因子（散乱ベクトルｋ（４πｓｉｎΘ／λ）の関数）
Ｓ ：構造因子（散乱ベクトルｋ（４πｓｉｎΘ／λ）の関数）
ここで、粒子の体積Ｖ、形状因子Ｐ、構造因子Ｓは、粒子の形状に関する数を構成するものである。&#61472; The particle model formula (basic formula of the scattering method) is expressed by the following formula.

Y2: intensity of scattered wave (electromagnetic wave) (function of scattering vector k (4πsinΘ / λ))
n: number density of particles V: volume of particles Δβ: difference in scattering length density P: particle shape factor (function of scattering vector k (4πsinΘ / λ))
S: Structure factor (function of scattering vector k (4πsinΘ / λ))
Here, the volume V, the shape factor P, and the structure factor S of the particles constitute numbers related to the shape of the particles. &#61472;

  Since each variable of the above-described particle model formula (Formula 1) varies depending on the shape of the particle, substituting the following formulas (Formula 2 to Formula 19) into the above-described particle model formula (Formula 1) depends on the shape of the particle. Each particle model formula can be determined.

希薄系の場合は、S=1であり、濃厚系の場合は、S≠1である。希薄系の場合と濃厚系の場合をそれぞれわけて計算する必要がある。 When the shape of the particle is a sphere, the equation substituted into the particle shape model equation (Equation 1) is expressed by the following equation.

In the case of a lean system, S = 1, and in the case of a rich system, S ≠ 1. It is necessary to calculate separately for the lean system and the rich system.

Ｒ：中空部分の球の半径
ｄ：厚さ
希薄系の場合は、S=1であり、濃厚系の場合は、 S≠1である。希薄系の場合と濃厚系の場合をそれぞれわけて計算する必要がある。 When the shape of the particle is a hollow sphere, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.

R: Radius of the sphere of the hollow portion d: Thickness In the case of a lean system, S = 1, and in the case of a rich system, S ≠ 1. It is necessary to calculate separately for the lean system and the rich system.

粒子濃度が、希薄系の場合は、S=1であり、濃厚系の場合は、 S≠1である。それぞれわけて計算する必要がある。 When the particle shape is a double-layered sphere, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.

If the particle concentration is lean, S = 1, and if it is dense, S ≠ 1. Each needs to be calculated separately.

a ：断面の円の半径
v ：短軸と長軸の軸比
粒子濃度が、希薄系の場合は、S=1であり、濃厚系の場合は、 S≠1である。それぞれわけて計算する必要がある。 When the cross section of the particle shape is an ellipsoid with a circle, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.

a: Radius of the circle of the cross section
v: Axis ratio between short axis and long axis When the particle concentration is dilute, S = 1, and when rich, S ≠ 1. Each needs to be calculated separately.

a：楕円体の中空部分の断面の円の半径
d：厚さ
v：短軸と長軸の軸比
粒子濃度が、希薄系の場合は、S=1であり、濃厚系の場合は、 S≠1である。それぞれわけて計算する必要がある。 In the case of an ellipsoid having a hollow particle shape and a circular cross section, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.

a: Radius of the circle of the cross section of the hollow part of the ellipsoid
d: thickness
v: Axis ratio between short axis and long axis When the particle concentration is dilute, S = 1, and when rich, S ≠ 1. Each needs to be calculated separately.

When the cross section of the particle shape is an ellipsoid of a double-layered circle, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.

a ：x 軸における長さ
b ：y 軸における長さ
c ：z 軸における長さ
粒子濃度が、希薄系の場合は、S=1であり、濃厚系の場合は、 S≠1である。それぞれわけて計算する必要がある。 When the cross section of the particle shape is an ellipsoid, the formula substituted into the particle model formula (Formula 1) is expressed by the following formula.

a: Length on the x axis
b: Length in y-axis
c: Length on the z-axis S = 1 when the particle concentration is lean, and S ≠ 1 when dense. Each needs to be calculated separately.

a ：楕円体の中空部分の断面の楕円のx 軸における長さ
b ：楕円体の中空部分の断面の楕円のy 軸における長さ
c ：楕円体の中空部分の断面の楕円のz 軸における長さ
d ：厚さ
粒子濃度が、希薄系の場合は、S=1であり、濃厚系の場合は、 S≠1である。それぞれわけて計算する必要がある。
In the case of an ellipsoid having a hollow particle shape and an elliptical cross section, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.

a: Length of the ellipsoid in the cross section of the hollow part on the x-axis of the ellipse
b: Length of the ellipsoid in the y-axis of the cross section of the hollow part
c: Length of the ellipsoid hollow section in the z-axis of the ellipse
d: Thickness When the particle concentration is lean, S = 1, and when it is dense, S ≠ 1. Each needs to be calculated separately.

When the cross section of the particle shape is an ellipsoid of a double layer ellipse, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.

（ｉｉ）濃厚系の場合
粒子濃度が濃い場合は、Random phase approxima tion (RPA) 近似とPolymer reference interaction site model (PRISM) 近似の二つが知られている。
（ｉｉ−１）RPA近似の場合

（ｉｉ−２）PRISM近似の場合

R ：底面の円の半径
H：円柱の高さ
J₁(x) ：第一次ベッセル関数
x ：任意のパラメータ When the shape of the particle is a cylinder, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.
(I) Dilute system

(Ii) In the case of a dense system When the particle concentration is high, there are two known Random phase approximation (RPA) approximation and Polymer reference interaction site model (PRISM) approximation.
(Ii-1) RPA approximation

(Ii-2) PRISM approximation

R: Radius of the bottom circle
H: Cylinder height
J ₁ (x): First-order Bessel function
x: Any parameter

（ｉｉ）濃厚系の場合
粒子濃度が濃い場合は、Random phase approxima tion (RPA) 近似とPolymer reference interaction site model (PRISM) 近似の二つが知られている。
（ｉｉ−１）RPA近似の場合

（ｉｉ−２）PRISM近似の場合

R ：底面の円の半径
d ：厚さ
H：円柱の高さ
J₁(x) ：第一次ベッセル関数
x ：任意のパラメータ When the shape of the particle is a hollow cylinder, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.
(I) Dilute system

(Ii) In the case of a dense system When the particle concentration is high, there are two known Random phase approximation (RPA) approximation and Polymer reference interaction site model (PRISM) approximation.
(Ii-1) RPA approximation

(Ii-2) PRISM approximation

R: Radius of the bottom circle
d: thickness
H: Cylinder height
J ₁ (x): First-order Bessel function
x: Any parameter

（ｉｉ）濃厚系の場合
粒子濃度が濃い場合は、Random phase approxima tion (RPA) 近似とPolymer reference interaction site model (PRISM) 近似の二つが知られている。
（ｉｉ−１）RPA近似の場合

（ｉｉ−２）PRISM近似の場合

When the particle shape is a double-layered cylinder, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.
(I) Dilute system

(Ii) In the case of a dense system When the particle concentration is high, there are two known Random phase approximation (RPA) approximation and Polymer reference interaction site model (PRISM) approximation.
(Ii-1) RPA approximation

(Ii-2) PRISM approximation

（ｉｉ）濃厚系の場合
粒子濃度が濃い場合は、Random phase approxima tion (RPA) 近似とPolymer reference interaction site model (PRISM) 近似の二つが知られている。
（ｉｉ−１）RPA近似の場合

（ｉｉ−２）PRISM近似の場合

a ：底面のx 軸における長さ
b ：底面のy軸における長さ
H：円柱の高さ When the shape of the particle is an elliptic cylinder, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.
(I) Dilute system

(Ii) In the case of a dense system When the particle concentration is high, there are two known Random phase approximation (RPA) approximation and Polymer reference interaction site model (PRISM) approximation.
(Ii-1) RPA approximation

(Ii-2) PRISM approximation

a: Bottom x-axis length
b: Length of bottom surface in y-axis
H: Cylinder height

（ｉｉ）濃厚系の場合
粒子濃度が濃い場合は、Random phase approxima tion (RPA) 近似とPolymer reference interaction site model (PRISM) 近似の二つが知られている。
（ｉｉ−１）RPA近似の場合

（ｉｉ−２）PRISM近似の場合

a ：底面のx 軸における長さ
b ：底面の y 軸における長さ
H：円柱の高さ
d：厚さである。 When the shape of the particle is a hollow elliptic cylinder, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.
(I) Dilute system

(Ii) In the case of a dense system When the particle concentration is high, there are two known Random phase approximation (RPA) approximation and Polymer reference interaction site model (PRISM) approximation.
(Ii-1) RPA approximation

(Ii-2) PRISM approximation

a: Bottom x-axis length
b: Bottom length on the y-axis
H: Cylinder height
d: Thickness.

（ｉｉ）濃厚系の場合
粒子濃度が濃い場合は、Random phase approxima tion (RPA) 近似とPolymer reference interaction site model (PRISM) 近似の二つが知られている。
（ｉｉ−１）RPA近似の場合

（ｉｉ−２）PRISM近似の場合

a ：底面のx 軸における長さ
b ：底面の y 軸における長さ
H：円柱の高さ
d：厚さである。 When the shape of the particle is a double-layered elliptic cylinder, the equation substituted into the particle model equation (Equation 1) is expressed by the following equation.
(I) Dilute system

(Ii) In the case of a dense system When the particle concentration is high, there are two known Random phase approximation (RPA) approximation and Polymer reference interaction site model (PRISM) approximation.
(Ii-1) RPA approximation

(Ii-2) PRISM approximation

a: Bottom x-axis length
b: Bottom length on the y-axis
H: Cylinder height
d: Thickness.

（ｉ）粒径分布が正規分布の場合は、次式であらわされるD(R)を上式に代入する。

R ：球の半径
Rav：平均粒径
σ^２：分散である。
（ｉｉ）粒径分布がシュルツ・ジム分布(Schultz-Zimm 分布)の場合は、次式であらわされるD(R)を上式に代入する。

R：球の半径
Rav ：平均粒径
σ^２：分散
Г(x) ：ガンマ関数
x ：任意の値

RmaxとRminは、Rmax＝Rav+０．１とRmin＝Rav−０．１と設定し、式（３５の５）を算出して、式（３５の３）の条件にならなければ、Rmax＝Rmax +０．１ とRmin＝Rmin−０．１を設定しなおして、式（３５の５）を算出する。この操作を式（３５の３）の条件になるまで繰り返して、式（３５の３）の条件を満たせば、RmaxとRminが決定される。 In the case of a multi-component sphere, the formula assigned to the particle model formula (Formula 1) is expressed by the following formula.

(I) When the particle size distribution is a normal distribution, D (R) expressed by the following equation is substituted into the above equation.

R: radius of the sphere
Rav: Average particle diameter σ ² : Dispersion.
(Ii) When the particle size distribution is a Schulz-Zimm distribution (Schultz-Zimm distribution), D (R) expressed by the following equation is substituted into the above equation.

R: radius of the sphere
Rav: average particle size σ ² : dispersion Γ (x): gamma function
x: Any value

Rmax and Rmin are set as Rmax = Rav + 0.1 and Rmin = Rav−0.1, the equation (35-5) is calculated, and if the condition of the equation (35-3) is not satisfied, Rmax = Re-set Rmax +0.1 and Rmin = Rmin−0.1, and calculate the equation (5 of 35). This operation is repeated until the condition of expression (35-3) is satisfied, and if the condition of expression (35-3) is satisfied, Rmax and Rmin are determined.

  The experimental graphing means (experimental spectrum calculating means) 9 calculates a scattering vector k (k = 4πsinΘ /) for each scattered light from the scattering angle (Θ) stored in the storage means 8 and the wavelength (λ) of the light applied to the particles. λ and π are circular ratios), and the calculated scattering vector (k) and the detected intensity (Y1) of the scattered light at the scattering angle (Θ) used for calculating the scattering vector (k) are used. Thus, an experimental graph is obtained with the scattering vector (k) on the horizontal axis and the intensity (Y) of scattered light on the vertical axis. The scattered light emitted from the particles differs depending on the angle irradiated to each particle, and the intensity (Y1) of the scattered light corresponding to each particle and the scattering angle (Θ) emitted from the scattered light are different. Detected. Then, the intensity (Y1) of the scattered light corresponding to each detected particle, the scattering angle (Θ) and the wavelength (λ) emitted from the scattered light are substituted into the relational expression k = (4πsinΘ / λ) of the scattering vector. Then, graphing is performed with the intensity of scattered light (Y) on the vertical axis and the scattering vector (k) on the horizontal axis.

  The particle model formula selection means 10 includes the above-described particle model formula stored in the storage means 8 (a particle model formula determined by the shape of the particle (a particle model formula obtained by substituting Formulas 2 to 19 into Formula 1)). The particle model formulas are selected one by one in a predetermined order from the above, whereby different particle model formulas (each particle model formula obtained by substituting Formulas 2 to 19 into Formula 1) depending on the shape of the particles are obtained. As described above, among the selected particle model equations at this stage, the number related to the shape of the particle, the number density (n) of the particles, and the scattering length density (Δβ) are unknown. In this embodiment, all the particle model formulas stored in the storage unit 8 are selected one by one, but not limited to this, all the particle model formulas stored in the storage unit 8 are selected. The selection may be made all at once, or may be divided and selected for each of a plurality of particle model expressions, and only some of the particle model expressions stored in the storage means 8 are selected. It is also possible to do it.

  The particle model formula initial value setting means 11 is an unknown number of particle model formulas in which the number related to the shape of the particle and the density of the particle is an unknown (number related to the shape of the particle, the number density of the particle (n), and the scattering length density (Δβ)). Is substituted with a predetermined (expected) initial value. Thereby, for the particle model formula selected by the particle model formula selection means 10, a predetermined number (initial value) is substituted for the unknown number of the particle model formula, and the particle model formula can be determined.

  The particle model formula setting graphing means 12 substitutes the scattering vector (k) calculated by the experimental graphing means 9 into the particle model formula into which the initial value has been substituted by the particle model formula initial value setting means 11, and performs scattering. The calculated light intensity (Y2) is calculated, and using the calculated scattered light scattering vector (k) and the calculated scattered light intensity (Y2), the scattered vector (k) is plotted on the horizontal axis. A particle model formula setting graph with the strength (Y) on the vertical axis is obtained. Thereby, the particle model formula setting graph of the particle model formula into which the initial value is substituted can be obtained.

  The graph difference squared minimum value storage unit 13 minimizes the square of the difference between the experimental graph obtained by the experimental graphing unit 9 and the particle model formula setting graph obtained by the particle model formula setting graphing unit 12. In this way, the number related to the particle shape and the density of the particle model equation is set, and the number of the set particle shape and the particle density is set to the minimum of the square of the difference between the experimental graph and the particle model equation setting graph. Remember the value. Specifically, first, the experimental graph obtained by the experimental graphing means 9 and the particle model formula setting graph obtained by the particle model formula setting graphing means 12 are compared. Then, the particle model formula initial value setting means 11 changes the number of the particle shape and the particle density to which the initial values are substituted, and the experimental graph and the particle model formula setting graph obtained by the experiment graphing means 9 are obtained. The number related to the particle shape and particle density in the particle model equation is determined so that the square of the difference in the particle model equation setting graph obtained by the means 12 is minimized. As a result, a graph that approximates the experimental graph can be obtained for the particle model formula selected by the particle model formula selection means 10.

  The particle shape estimation unit 14 is configured to minimize the graph difference squared for the particle model formula setting graph of all the particle model formulas selected by the particle model formula selection unit 10 (particle model formulas obtained by substituting the formulas 2 to 19 into the formula 1). The minimum value of the square of the difference between the experimental graph stored by the value storage means 13 and the particle model formula setting graph is compared, and the particle model formula having the smallest difference is selected. As a result, among the particle model formula setting graphs of all the particle model formulas selected by the particle model formula selection means 10, it is possible to obtain a graph that most closely approximates the experimental graph. Then, the particle shape is estimated from the particle model equation, and the particle size can be estimated from the number related to the particle size of the particle model equation set by the graph difference square minimum value storage means 13. In the present embodiment, the shape and size of the particles are obtained, but only the shape of the particles may be obtained.

  Next, the particle shape estimation method of the present invention will be described with reference to FIG. FIG. 2 is a flowchart of a particle shape estimation method according to an embodiment of the present invention.

  In S11, it is determined whether the power switch (not shown) of the X-ray generation source 2 is ON. If YES is determined in S11, it is determined in S12 whether the wavelength of the X-ray irradiated to the particle is input. The wavelength of X-rays irradiated on the particles is input by an X-ray wavelength input unit (not shown). In the present embodiment, the X-ray wavelength input unit is used to input the X-ray wavelength input unit. However, the present invention is not limited to this, and the X-ray wavelength input unit is not provided. The particles may be irradiated with X-rays having a wavelength. In this embodiment, particles are irradiated with X-rays. However, the present invention is not limited to this, and neutrons or the like may be used. If YES is determined in S12, the process proceeds to S13.

  In S13, it is determined whether an X-ray emission switch (not shown) is turned on. If YES in S13, the process proceeds to S14. In addition, although this embodiment demonstrated the aspect which each provided the power switch and the X-ray emission switch separately, not only this but a power switch and an X-ray emission switch may serve as one switch.

  In S <b> 14, X-rays are emitted toward the particles in the liquid in the container 4. Specifically, X-rays emitted from the X-ray generation source 2 are irradiated to particles in the liquid via the slit 3. The X-rays irradiated toward the particles are scattered and become scattered light by hitting the particles. Since a plurality of particles are present in the liquid, scattered light is generated for each particle.

  In S15, the detector 6 detects the intensity (intensity (Y1)) of the light (scattered light) scattered by the particles and the scattering angle (Θ) of the scattered light. Specifically, the detector 6 has a plurality (256 in the present embodiment) of scattered light detectors (not shown) for detecting scattered light, and the scattered light is detected by each scattered light detector. Intensity (Y1) and scattering angle (Θ) are detected. Since there are a plurality of particles irradiated with X-rays, the light intensity (Y1) of the scattered light and the scattering angle (Θ) are detected in association with each particle. As described above, the scattering angle (Θ) detected by the scattered light detection unit has a specific value for each scattered light detection unit, so the scattering angle (Θ) detected by the scattered light detection unit is not used. Alternatively, the scattering angle (Θ) of each scattered light detection unit stored in the storage unit 8 may be used.

  In S16, the detected scattered light intensity (Y1) and scattering angle (Θ) are stored in the storage means 8. Since there are a plurality of particles irradiated with X-rays, the light intensity (Y1) of the scattered light and the scattering angle (Θ) are stored in association with each other.

  In S17, using the wavelength (λ) of the light irradiated to the particle from the X-ray generation source 2 and the respective scattering angles (Θ) of the scattered light stored in the storage unit 8, the scattering vector for each scattered light. k (k = 4π sin Θ / λ, where π is the circumference) is calculated. Then, using the calculated scattering vector (k) and the detected intensity (Y1) of the scattered light at the scattering angle (Θ) used for the calculation of the scattering vector (k), the scattering vector (k) is plotted on the horizontal axis. In addition, an experimental graph (see FIG. 3) in which the intensity (Y) of scattered light is plotted on the vertical axis is obtained. That is, the scattered light scattered from the particles varies depending on the angle of the X-rays irradiated to the respective particles, and the scattered light intensity (Y1) corresponding to each particle and the scattering angle emitted from the scattered light ( Θ) is detected. Then, using the scattering vector (k) obtained from the scattered light intensity (Y1) and the scattering angle (Θ) corresponding to each detected particle, the horizontal axis represents the scattering vector (k), and the vertical axis represents An experimental graph (see FIG. 3) is obtained by taking the intensity (Y) of the scattered light. As described above, the scattering angle (Θ) of scattered light and the intensity (Y1) of scattered light are detected by the detector 6, but the detector 6 detects a scattered light detector (for detecting the scattered light). There are a plurality (not shown) (256 in the present embodiment), and the scattered light intensity (Y1) and the scattering angle (Θ) are detected by the respective scattered light detectors. Therefore, the scattering angle (Θ) detected by each scattered light detection unit is the scattering angle (Θ) determined for each scattered light detection unit. Here, as can be seen from FIG. 3, the intensity (Y1) corresponding to the scattering vector (k) obtained from each scattering angle (Θ) is obtained. FIG. 3 is a diagram showing an experimental graph in one embodiment of the present invention.

  In S18, the particle model formula determined by the shape of the particles (spherical particles, hollow sphere particles, etc.) stored in the storage means 8, that is, the formulas 2 to 19 are substituted into the formula 1 respectively. One by one is selected from the particle model formula in a predetermined order. Thereby, different particle model formulas (each particle model formula obtained by substituting Formulas 2 to 19 into Formula 1) are selected depending on the shape of the particles. At this stage, the selected particle model equation is in a state where the number related to the shape of the particle, the number density (n) of the particles, and the scattering length density (Δβ) are unknown. In the present embodiment, a case where a dilute particle model formula (formula obtained by substituting Formula 19 into Formula 1) having a double-layered column shape is selected will be described.

In S19, the dilute particle model formula of the double-layer cylinder selected in S18 is a number related to the shape of the particle and a number related to the density of the particles (R (radius of the bottom circle), d (thickness), H (cylinder). ), Βcore (scattering length density of the central part of the particle), βshell (scattering length density of the outer part of the particle), and n (number density of the particle)) are unknown numbers, A predetermined (expected) initial value is assigned to the unknown. Specifically, 5 × 10 ⁻¹⁶ is substituted as an initial value of n (particle number density), and 8.026 μÅ− ² is substituted as an initial value of β _core (scattering length density of the central portion of the particle). The initial value of β _shell (scattering length density of the outer part of the particle) is substituted with 9.697 μÅ− ² , the initial value of β _solvent (scattering length density of solvent) is substituted with 9.216 μÅ− ² , and R (bottom surface). 33 代 入 is substituted as the initial value of the radius of the circle, and 20 代 入 is substituted as the initial value of H (the height of the cylinder). In addition, “1” is substituted for S (structural factor) (see Formula 19-2). As a result, for the particle model formula selected by the particle model formula selection means 10, a predetermined number (initial value) is substituted for the unknown number of the particle model formula, and a particle model formula without an unknown number can be determined.

  In S20, the scattered light calculated intensity (Y2) is calculated by substituting the scattering vector (k) calculated in S17 into the particle model equation in which the initial value is substituted in S19. Then, using the calculated scattering vector (k) of the scattered light and the calculated intensity (Y2) of the scattered light, the particle having the scattering vector (k) on the horizontal axis and the intensity (Y) of the scattered light on the vertical axis. A model formula setting graph is required. Thereby, a particle model formula setting graph of the particle model formula into which the initial value is substituted is obtained (not shown). This particle model equation setting graph is a particle model equation setting graph of a dilute particle model equation in which the particle shape is a double-layered cylinder.

  In S21, the number (R (bottom surface) of particle shape and particle density in the particle model equation is set so that the square of the difference between the experimental graph obtained in S17 and the particle model equation setting graph obtained in S20 is minimized. ), D (thickness), H (cylinder height), βcore (scattering length density in the central part of the particle), βshell (scattering length density in the outer part of the particle), and n (number of particles) Density)) is set. In other words, the number of particle shape and initial density (R (radius of the bottom circle)), d (thickness), H (cylinder height), β core (scattering at the center of the particle) (Long density), β shell (scattering length density of the outer part of the particle), and n (number density of the particle)), the experimental graph obtained by S17 and the particle model formula setting graph obtained by S20 The square of the difference is minimized. This is performed by computer processing using a simplex method (also known as a polytope method), a Gauss-Jordan method, or the like. Then, the number (R (radius of the bottom circle)), d (thickness), H (cylinder height), βcore (scattering of the central part of the particle) regarding the set (changed) particle shape and particle density. (Long density), β shell (scattering length density of the outer portion of the particle), and n (number density of the particle)) and the square of the difference between the experimental graph and the particle model formula setting graph are stored. Specifically, the experimental graph obtained in S17 and the particle model formula setting graph obtained in S20 are compared, and the number ((R (bottom surface) of the particle shape and particle density into which the initial values are substituted in S20). ), D (thickness), H (cylinder height), βcore (scattering length density in the central part of the particle), βshell (scattering length density in the outer part of the particle), and n (number of particles) The density of the particles in the particle model formula is minimized so that the sum of the squares of the differences between the individual values in the experimental graph obtained in S17 and the particle model formula setting graph obtained in S20 is minimized. Number related to shape and particle density ((R (radius of the bottom circle), d (thickness), H (cylinder height), βcore (scattering length density at the center of the particle), βshell (outer part of the particle) Scattering length density) and n (number density of particles)) As a result, a graph that approximates the experimental graph is obtained for the particle model formula selected in S18 (see FIG. 4), where FIG. It is a figure which shows the dilute type | system | group granulation model type | formula setting graph of a double layer cylinder.

  In S22, it is determined whether all the particle model formulas have been selected. That is, it is determined that all the particle model formulas stored in the storage unit 8 (particle model formulas obtained by substituting Formulas 2 to 19 into Formula 1) have been selected in the particle model formula selection step of S18. In this embodiment, it is determined whether all the particle model formulas stored in the storage unit 8 are selected. However, the present invention is not limited to this, and some particle model formulas stored in the storage unit 8 are selected. In the case of doing so, it is judged whether all of the partial particle models have been selected. If all the particle model formulas are not selected, the process returns to S18, and the processes of S18 → S19 → S20 → S21 → S22 → S18 are performed until all the particle model formulas are selected. If it is determined in S22 that all the particle model formulas have been selected, the process proceeds to S23.

  In S23, for the particle model formula setting graph of all the particle model formulas selected in S18 (particle model formulas obtained by substituting Formulas 2 to 19 into Formula 1), the experiment stored by the graph difference square minimum value storage unit 13 The minimum value (total value) of the square of the difference between the conversion graph and the particle model equation setting graph is compared, and the particle model equation having the smallest value is selected. As a result, among the particle model formula setting graphs of all the particle model formulas selected in S18, a graph that most closely approximates the experimental graph can be obtained. In the present embodiment, the particle model formula having the smallest difference squared is the double-layered cylinder (see FIG. 5). For convenience of explanation, FIG. 5 does not graph all the particle model expressions stored in the storage unit 8. Then, the shape of the particle (in this embodiment, a dilute system of a double-layer cylinder) is estimated from the particle model formula having the smallest square of the difference, and the value stored in the graph difference square minimum value storage unit 13 is estimated. The particle size ((R (radius of the bottom circle), d (thickness), H (cylinder height)) is estimated from the number related to the particle size in the particle model formula, where FIG. These are the figures which compared the experimental graph and each particle model type | formula setting graph in one Embodiment of this invention.

  As described above, according to the present invention, the minimum value of the sum of the squares of the differences between the experimental graph and the particle model formula setting graph is obtained for all the particle model formulas selected in the particle model formula selection step 18. The particle model formula having the smallest value among the minimum values can be selected, and the shape of the particle can be estimated from the particle model formula, and the particle size can be estimated from the number related to the particle size of the particle model formula. Can be estimated. Thereby, not only the shape of the particle | grains in a liquid but various sizes accompanying the shape of the particle | grain can be clarified.

It is a block diagram of the particle shape estimation apparatus used for the particle shape estimation method in one embodiment of the present invention. It is a flowchart of the particle shape estimation method. It is a figure which shows the experimental graph in one Embodiment of this invention. It is a figure which shows the particle-ized model type | formula setting graph of the dilute type | system | group of a double layer cylinder when the square value in one Embodiment of this invention is the minimum. It is the figure which compared the experimental graph and each particle model type | formula setting graph in one Embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Particle shape estimation apparatus 2 X-ray generation source 3 Slit 4 Container 5 Vacuum path 6 Detector 7 Computer part 8 Storage means 9 Experiment graphing means 10 Particle model formula selection means 11 Particle model formula initial value setting means 12 Particle model formula setting Graphing means 13 Graph difference square minimum value storage means 14 Particle shape estimation means

Claims (5)

A particle shape estimation method for estimating the shape of particles dispersed in a liquid,
A light irradiation step of irradiating particles in the liquid with light;
A scattered light detection step for detecting scattered light scattered from the particles;
A storage step for storing the detection intensity (Y1) and the scattering angle (Θ) of each scattered light detected by the scattered light detection step for each scattered light;
Scattering vector k (k = 4π sin Θ / λ, π is the pi) for each scattered light from the scattering angle (Θ) stored in the storage step and the wavelength (λ) of the light irradiated on the particles in the light irradiation step. The scattered vector (k) and the detected intensity (Y1) of scattered light for each scattering angle (Θ) used for calculating the scattered vector (k) An experimental graphing step for obtaining an experimental graph with the detected intensity (Y) of scattered light as the vertical axis on the axis;
A particle model expression representing the intensity (Y) of scattered light with the scattering vector (k) as a variable, and different particle model expressions are stored in advance in the storage means depending on the shape of the particles, and the particles stored in the storage means A particle model formula selection step for selecting a model formula;
The initial value of the particle model formula that is selected in the particle model formula selection step and sets the particle model formula by substituting a predetermined initial value for the unknown number of the particle model formula with the number related to the particle shape and the density of the particle as an unknown. Configuration steps;
The scattered light calculated intensity (Y2) is calculated by substituting the scattering vector (k) calculated in the experimental graphing step into the particle model equation in which the initial value is assigned in the particle model equation initial value setting step. Then, using the scattering vector (k) and the calculated intensity (Y2) of the scattered light, a particle model equation setting graph with the scattering vector (k) on the horizontal axis and the scattered light intensity (Y) on the vertical axis is shown. The desired particle model formula setting graphing step,
Particle shape and particle shape of the particle model formula so that the square of the difference between the experimental graph obtained in the experimental graphing step and the particle model formula setting graph obtained in the particle model formula setting graph step is minimized. A graph difference squared minimum value that stores a number relating to the density of the particle, a number relating to the set particle shape and particle density, and a minimum square value of the difference between the experimental graph and the particle model formula setting graph A memory step;
For all the particle model formulas selected in the particle model formula selection step, the first of the minimum square values of the differences between the experimental graph stored in the graph difference square minimum value storage step and the particle model formula setting graph is the first. A particle shape estimation step of selecting a particle model equation having a small value and estimating the shape of the particle from the particle model equation;
A particle shape estimation method comprising: A particle shape estimation method for estimating the shape of particles dispersed in a liquid and the size of the shape,
A light irradiation step of irradiating particles in the liquid with light;
A scattered light detection step for detecting scattered light scattered from the particles;
A storage step for storing the detection intensity (Y1) and the scattering angle (Θ) of each scattered light detected by the scattered light detection step for each scattered light;
Scattering vector k (k = 4π sin Θ / λ, π is the pi) for each scattered light from the scattering angle (Θ) stored in the storage step and the wavelength (λ) of the light irradiated on the particles in the light irradiation step. The scattered vector (k) and the detected intensity (Y1) of scattered light for each scattering angle (Θ) used for calculating the scattered vector (k) An experimental graphing step for obtaining an experimental graph with the detected intensity (Y) of scattered light as the vertical axis on the axis;
A particle model expression representing the intensity (Y) of scattered light with the scattering vector (k) as a variable, and different particle model expressions are stored in advance in the storage means depending on the shape of the particles, and the particles stored in the storage means A particle model formula selection step for selecting a model formula;
The initial value of the particle model formula that is selected in the particle model formula selection step and sets the particle model formula by substituting a predetermined initial value for the unknown number of the particle model formula with the number related to the particle shape and the density of the particle as an unknown. Configuration steps;
The scattered light calculated intensity (Y2) is calculated by substituting the scattering vector (k) calculated in the experimental graphing step into the particle model equation in which the initial value is assigned in the particle model equation initial value setting step. Then, using the scattering vector (k) and the calculated intensity (Y2) of the scattered light, a particle model equation setting graph with the scattering vector (k) on the horizontal axis and the scattered light intensity (Y) on the vertical axis is shown. The desired particle model formula setting graphing step,
Particle shape and particle shape of the particle model formula so that the square of the difference between the experimental graph obtained in the experimental graphing step and the particle model formula setting graph obtained in the particle model formula setting graph step is minimized. A graph difference squared minimum value that stores a number relating to the density of the particle, a number relating to the set particle shape and particle density, and a minimum square value of the difference between the experimental graph and the particle model formula setting graph A memory step;
For all the particle model formulas selected in the particle model formula selection step, the first of the minimum square values of the differences between the experimental graph stored in the graph difference square minimum value storage step and the particle model formula setting graph is the first. A particle model equation having a small value is selected, the shape of the particle is estimated from the particle model equation, and the particle size is determined from the number related to the particle size of the particle model equation set by the graph difference square minimum value storing step. A particle shape estimation step for estimating the thickness;
A particle shape estimation method comprising: In the particle model formula initial value setting step, Y = n × Δβ ² × V ² × P × S (where n is the number density of particles and V is the volume of particles) .DELTA..beta. Is the difference between the scattering length densities of the particles and the solvent, P is the particle shape factor (a function of the scattering vector k), and S is the structure factor (a function of the scattering vector k). The particle shape estimation method described.   In the experiment graphing step, a scattering vector (k = 4πsinΘ / λ, where π is a circumference ratio) is calculated based on a wavelength (λ) and a scattering angle (Θ) of light irradiated on a particle stored in advance. The particle shape estimation method according to claim 1 or 2, characterized in that The particle shape estimation method according to claim 1 or 2, wherein the light irradiated into the liquid in the light irradiation step is X-rays or neutrons.

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