Particle measuring device and particle measuring method

Abstract

Provided are a particle measurement device and particle measurement method that make it possible to measure the refractive index or complex refractive index and the particle size distribution of a single type of particle included in a dispersion. This particle measurement device comprises a light source unit that emits measurement light onto a dispersion including a single type of particle, a parameter setting unit that sets at least one from among a scattering angle and measurement wavelength as a measurement parameter, a scattered light measurement unit that obtains a plurality of items of scattering intensity data by changing the set values of the measurement parameter and repeatedly measuring the scattering intensity of scattered light emitted from the dispersion as a result of the measurement light, and a computation unit that calculates time variation characteristic data for the scattering intensity and parameter dependence data for the scattering intensity from the plurality of items of scattering intensity data and determines the refractive index and particle size distribution of the single type of particle by subjecting the calculated time variation characteristic data for the scattering intensity and parameter dependence data for the scattering intensity to fitting using a theoretical formula defining the relationship between the refractive index, particle size, and scattering intensity or a simulation based on electromagnetic wave behavior theory.

Description

[Technical Field]

[0001] The present invention relates to a particle measuring device and a particle measuring method for measuring the refractive index of a single type of particle contained in a dispersion. [Background technology]

[0002] Dynamic light scattering is a method for investigating the dynamic properties of a scattering material by shining light onto a medium such as a colloidal solution or particle dispersion and detecting the time variation of the scattered light intensity from the scattering material in the medium using an autocorrelation function or power spectrum. Dynamic light scattering is widely used for various measurements, such as particle size measurement and gel structure analysis.

[0003] For example, Patent Document 1 describes a particle size measuring device comprising: a laser device that irradiates a group of particles to be measured with a laser beam; a measurement system that measures the intensity of scattered light at each scattering angle as a scattered light intensity distribution, emitted from the laser device and scattered by the group of particles to be measured; a relative particle size distribution calculation means that calculates a relative particle size distribution from the measured values ​​of the scattered light intensity distribution obtained by the measurement system; a conversion table that stores conversion coefficients obtained by calculating the ratio of the measured values ​​of the scattered light intensity distribution obtained by irradiating a group of reference particles with known particle size and particle size density with a laser beam to the same theoretical values ​​for each scattering angle; a conversion means that converts the measured values ​​of the scattered light intensity distribution obtained by irradiating a group of particles to be measured with a laser beam based on the conversion table to obtain an incident scattered light intensity distribution at the incident part of the measurement system; and an absolute particle size distribution calculation means that calculates an absolute particle size distribution from the incident scattered light intensity distribution obtained by the conversion means and the relative particle size distribution of the group of particles to be measured obtained by the relative particle size distribution calculation means. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Special Publication No. 2-63181 [Overview of the project] [Problems that the invention aims to solve]

[0005] As described above, Patent Document 1 describes calculating the absolute particle size distribution using the scattered light intensity distribution, which is the intensity of scattered light at each scattering angle scattered by the group of particles being measured. However, while Patent Document 1 can measure the particle size distribution, it cannot measure the refractive index of the particles. There is a need to obtain refractive index information for the particles being measured, but currently, this information cannot be obtained.

[0006] The object of the present invention is to provide a particle measuring device and a particle measuring method that can measure the refractive index or complex refractive index and particle size distribution of a single type of particle contained in a dispersion. [Means for solving the problem]

[0007] To achieve the above objective, the invention [1] provides a particle measuring device for a dispersion containing a single type of particle, comprising: a light source unit that irradiates the dispersion with measuring light; a parameter setting unit that sets at least one of scattering angle and measurement wavelength as a measurement parameter; a scattered light measuring unit that changes the values ​​of the measurement parameter set by the parameter setting unit multiple times and measures the scattering intensity of the scattered light emitted from the dispersion by the measuring light multiple times to obtain multiple scattering intensity data; and a calculation unit that calculates time variation characteristic data of scattering intensity and parameter-dependent data of scattering intensity from the multiple scattering intensity data obtained by the scattered light measuring unit, and determines the refractive index and particle size distribution of a single type of particle by fitting the calculated time variation characteristic data of scattering intensity and parameter-dependent data of scattering intensity using a theoretical formula that defines the relationship between refractive index, particle size, and scattering intensity or a simulation based on the theory of electromagnetic wave behavior.

[0008] The invention [2] provides a particle measuring device for a dispersion containing a single type of particle, comprising: a light source unit that irradiates the dispersion with measurement light; a parameter setting unit that sets at least one of scattering angle and measurement wavelength as a measurement parameter; a scattered light measurement unit that changes the values ​​of the measurement parameter set by the parameter setting unit multiple times and measures the scattering intensity of the scattered light emitted from the dispersion by the measurement light multiple times to obtain multiple scattering intensity data; and a calculation unit that calculates time variation characteristic data of scattering intensity and parameter-dependent data of scattering intensity from the multiple scattering intensity data obtained by the scattered light measurement unit, and fits the calculated time variation characteristic data of scattering intensity, parameter-dependent data of scattering intensity and transmittance data of the dispersion using a theoretical formula defining the relationship between complex refractive index, particle size, and scattering intensity or a simulation based on the theory of electromagnetic wave behavior, and a theoretical formula defining the relationship between complex refractive index, particle size, and transmittance or a simulation based on the theory of electromagnetic wave behavior to determine the complex refractive index and particle size distribution of a single type of particle. Invention [3] is a particle measuring device according to Invention [2], having a transmittance measuring unit for measuring the transmittance of a dispersion.

[0009] Invention [4] is a particle measuring device according to any one of Inventions [1] to [3], wherein the measurement parameter is the scattering angle, and the scattered light measuring unit changes the value of the scattering angle by two or more angles to measure the scattering intensity of the scattered light of the dispersion at multiple scattering angles and obtain multiple scattering intensity data. Invention [5] is a particle measuring device according to any one of Inventions [1] to [3], wherein the measurement parameter is the measurement wavelength, and the scattered light measuring unit uses two or more measurement wavelengths to measure the scattering intensity of scattered light from a dispersion at multiple measurement wavelengths to obtain multiple scattering intensity data. Invention [6] is a particle measuring device according to any one of Inventions [1] to [5], wherein the scattered light measuring unit measures the light intensity of the polarization component of the scattered light of a dispersion obtained by irradiating the dispersion with measuring light of a specific polarization as the scattering intensity. Invention [7] is a particle measuring device according to any one of Inventions [1] to [6], wherein the scattered light measuring unit measures at least one of parameter-dependent data of scattering intensity obtained by sequentially irradiating a dispersion with measurement light in multiple polarization states, and parameter-dependent data of scattering intensity obtained by extracting multiple polarization components of scattered light emitted from the dispersion. Invention [8] is a particle measuring device according to any one of Inventions [1] to [7], wherein the time variation characteristic data of the calculated scattering intensity of the measurement parameters is calculated based on the Stokes-Einstein theoretical formula, and the parameter-dependent data of the scattering intensity of the measurement parameters is calculated based on at least one of the Mie scattering theory, the discrete dipole approximation method, and the finite difference time-domain method. Invention [9] is a particle measuring device according to Invention [1] and any one of [4] to [8], wherein the calculation unit compares the refractive index of a single type of particle with the refractive index of a known material at 100% concentration and calculates the volume concentration of the constituent material of the single type of particle using the dependence of the refractive index on the particle volume concentration. Invention

[10] is a particle measuring device according to Invention [2], wherein the calculation unit determines the complex refractive index and the particle size distribution of the number concentration of a single type of particle by fitting the time variation characteristic data of the scattering intensity, the parameter-dependent data of the scattering intensity, the transmittance data, and the volume concentration data of the dispersion.

[0010] The invention

[11] provides a method for measuring particles in a dispersion containing a single type of particle, wherein at least one of scattering angle and measurement wavelength is set as a measurement parameter, and the scattering intensity of scattered light emitted from the dispersion by the measurement light is measured multiple times by changing the value of the set measurement parameter multiple times; a calculation step of calculating time variation characteristic data of scattering intensity and parameter-dependent data of scattering intensity from the multiple scattering intensity data obtained in the measurement step; a step of fitting the time variation characteristic data of scattering intensity and parameter-dependent data of scattering intensity obtained in the calculation step using a theoretical formula that defines the relationship between refractive index, particle size and scattering intensity or a simulation based on the theory of electromagnetic wave behavior; and a step of determining the refractive index and particle size distribution of a single type of particle in the dispersion.

[0011] The invention

[12] provides a method for measuring particles in a dispersion containing a single type of particle, wherein at least one of scattering angle and measurement wavelength is set as a measurement parameter, and the scattering intensity of scattered light emitted from the dispersion by the measurement light is measured multiple times by changing the value of the set measurement parameter multiple times; a calculation step of calculating time variation characteristic data of scattering intensity and parameter-dependent data of scattering intensity from multiple scattering intensity data obtained in the measurement step; and a step of determining the complex refractive index and particle size distribution of a single type of particle by fitting the transmittance data of the dispersion, the time variation characteristic data of scattering intensity and the parameter-dependent data of scattering intensity obtained in the calculation step, using a theoretical formula defining the relationship between complex refractive index, particle size and scattering intensity or a simulation based on the theory of electromagnetic wave behavior, and a theoretical formula defining the relationship between complex refractive index, particle size and transmittance or a simulation based on the theory of electromagnetic wave behavior. Invention

[13] is a method for measuring particles according to Invention

[12] , comprising the step of measuring the transmittance of a dispersion and obtaining transmittance data.

[0012] Invention

[14] is a method for measuring particles according to any one of Inventions

[11] to

[13] , wherein the measurement parameter is a scattering angle, and the measurement step is to change the value of the scattering angle by two or more angles and measure the scattering intensity of the scattered light of the dispersion for each of the multiple scattering angles. Invention

[15] is a method for measuring particles according to any one of Inventions

[11] to

[13] , wherein the measurement parameter is the measurement wavelength, and the measurement step is to measure the scattering intensity of scattered light of a dispersion at multiple measurement wavelengths using two or more measurement wavelengths. Invention

[16] is a method for measuring particles according to any one of Inventions

[11] to

[15] , wherein the measurement step is to irradiate the dispersion with measurement light of a specific polarization and measure the light intensity of the polarization component of the scattered light of the dispersion obtained as the scattering intensity. Invention

[17] is a method for measuring particles according to any one of Inventions

[11] to

[16] , wherein the measurement step measures at least one of parameter-dependent data of scattering intensity obtained by sequentially irradiating a dispersion with measurement light in multiple polarization states, and parameter-dependent data of scattering intensity obtained by extracting multiple polarization components of scattered light emitted from the dispersion. The invention

[18] is a method for measuring particles according to any one of the inventions

[11] to

[17] , wherein the time variation characteristic data of the scattering intensity of the calculated measurement parameters are calculated based on the Stokes-Einstein theoretical formula, and the parameter-dependent data of the scattering intensity of the measurement parameters are calculated based on at least one of the Mie scattering theory, the discrete dipole approximation method, and the finite difference time-domain method. The invention

[19] further comprises the steps of comparing the refractive index of a single type of particle to be determined with the refractive index of a known material at 100% concentration, and using the dependence of the refractive index on the particle volume concentration to calculate the volume concentration of the constituent material of the single type of particle to be determined. This is the method for measuring particles according to any one of the inventions

[11] and

[14] to

[18] . Invention

[20] is a particle measurement method according to Invention

[12] , which determines the complex refractive index and particle size distribution of a single type of particle by fitting it with time variation characteristic data of scattering intensity, parameter-dependent data of scattering intensity, transmittance data, and volume concentration data of the dispersion. [Effects of the Invention]

[0013] According to the present invention, it is possible to provide a particle measuring device and a particle measuring method that can measure the refractive index or complex refractive index and particle size distribution of a single type of particle contained in a dispersion. [Brief explanation of the drawing]

[0014] [Figure 1] This is a schematic diagram showing a first example of a particle measuring device according to an embodiment of the present invention. [Figure 2] This flowchart shows a first example of a particle measurement method according to an embodiment of the present invention. [Figure 3] This graph shows an example of the relationship between the scattering intensity and scattering angle of an aqueous dispersion of polystyrene particles. [Figure 4] This graph shows an example of a second-order autocorrelation function for each scattering angle. [Figure 5] This graph shows the calculated scattering angle and scattering intensity for particles of the same size, for each refractive index. [Figure 6] This graph shows an example of the relationship between scattering intensity and measurement wavelength. [Figure 7] This graph shows another example of the relationship between scattering intensity and measured wavelength. [Figure 8] This graph shows the relationship between scattering intensity and scattering angle for each particle shape. [Figure 9] This is a schematic diagram showing a second example of a particle measuring device according to an embodiment of the present invention. [Figure 10] This is a schematic diagram showing a third example of a particle measuring device according to an embodiment of the present invention. [Figure 11] This is a histogram of the particles. [Figure 12]This flowchart shows a second example of a particle measurement method according to an embodiment of the present invention. [Figure 13] This is a schematic diagram showing a fourth example of a particle measuring device according to an embodiment of the present invention. [Figure 14] This graph shows the particle size distribution of polystyrene particles. [Figure 15] This graph shows the relationship between the scattering intensity and scattering angle of polystyrene particles. [Figure 16] This graph shows the second-order autocorrelation function of polystyrene particles. [Figure 17] This graph shows the particle size distribution of titanium dioxide particles. [Figure 18] This graph shows the relationship between the scattering intensity and scattering angle of titanium dioxide particles. [Figure 19] This graph shows the second-order autocorrelation function of titanium dioxide particles. [Figure 20] This graph shows the particle size distribution of sample 3. [Figure 21] This graph shows the relationship between the scattering intensity and scattering angle for sample 3. [Figure 22] This graph shows the second-order autocorrelation function of sample 3 at a scattering angle of 50°. [Figure 23] This graph shows the second-order autocorrelation function of sample 3 at a scattering angle of 90°. [Figure 24] This graph shows the second-order autocorrelation function of sample 3 at a scattering angle of 150°. [Figure 25] This graph shows the transmittance of Sample 3. [Modes for carrying out the invention]

[0015] The particle measuring apparatus and particle measuring method of the present invention will be described in detail below based on preferred embodiments shown in the attached drawings. The figures described below are illustrative examples for illustrating the present invention, and the present invention is not limited to the figures shown below. In the following, the "~" indicating a numerical range includes the numbers written on both sides. For example, ε is the numerical value ε A ~Value ε B Therefore, the range of ε is the numerical value ε A and the numerical value ε B This range includes ε A ≦ε≦ε B That is the case. Unless otherwise specified, angles expressed as "specific numerical values" and angles such as "perpendicular" include the generally acceptable margin of error in the relevant technical field.

[0016] (First example of a particle measuring device) Figure 1 is a schematic diagram showing a first example of a particle measuring device according to an embodiment of the present invention. The particle measuring device 10 shown in Figure 1 includes an incident setting unit 12 that irradiates a sample cell 16 containing a dispersion Lq of a single type of particle with laser light as measurement light, a scattered light measuring unit 14 that measures the scattering intensity of scattered light produced when the laser light is scattered by the dispersion Lq, and a calculation unit 18 that determines the refractive index and particle size distribution of the single type of particle contained in the dispersion. The complex refractive index has a real part and an imaginary part. The real part of the complex refractive index is what is commonly called the refractive index. The imaginary part of the complex refractive index is called the extinction coefficient, which represents absorption. The imaginary part of the complex refractive index is close to zero when the transmittance of the particle is high.

[0017] The incident setting unit 12 includes a first light source unit 20 that emits laser light as measurement light to the dispersion Lq, a second light source unit 22 that emits laser light as measurement light to the dispersion Lq, a half mirror 24, a focusing lens 26 that focuses the laser light transmitted or reflected by the half mirror 24 onto the sample cell 16, and a polarizing element 28 that transmits only a certain polarization component of the laser light. A first shutter 21a is provided between the first light source unit 20 and the half mirror 24. A second shutter 21b is provided between the second light source unit 22 and the half mirror 24. The first shutter 21a prevents the laser light emitted from the first light source unit 20 from entering the half mirror 24 or shields it from entering. The second shutter 21b prevents the laser light emitted from the second light source unit 22 from entering the half mirror 24 or shields it from entering. The first shutter 21a and the second shutter 21b are not particularly limited as long as they can direct the emitted laser light into the half mirror 24 or block it; known opening and closing shutters used for controlling the emission of laser light can be used. In addition to providing the first shutter 21a and the second shutter 21b, the emission of laser light to the half mirror 24 may also be controlled by controlling the emission from the first light source unit 20 and the emission from the second light source unit 22, for example.

[0018] The half-mirror 24 transmits the laser light emitted from the first light source unit 20 and reflects the laser light emitted from the second light source unit 22 at, for example, 90° with respect to the incident direction, and along the same optical path as the laser light emitted from the first light source unit 20. The laser light transmitted through the half-mirror 24 and the laser light reflected by the half-mirror 24 pass along the same optical axis C1. A focusing lens 26 and a polarizing element 28 are arranged on the optical axis C1. A sample cell 16 is arranged on the optical axis C1. Furthermore, a shutter (not shown) that temporarily blocks the optical path of the laser beam and an ND (Neutral Density) filter (not shown) that attenuates the laser beam may be provided on the optical axis C1 of the laser beam. ND filters are used to adjust the intensity of laser light, and any known type can be used as appropriate.

[0019] The polarizing element 28 can be any polarizing element appropriate to the polarization of light irradiated onto the sample cell 16, such as circularly polarized, linearly polarized, or elliptically polarized light. Note that if it is not necessary to irradiate the sample cell 16 with polarized light, the polarizing element 28 is not necessarily required.

[0020] The first light source unit 20 irradiates the dispersion Lq with laser light as measurement light to the dispersion Lq, and is, for example, an Ar laser that emits laser light with a wavelength of 488 nm. The wavelength of the laser light is not particularly limited. The second light source unit 22 irradiates the dispersion Lq with laser light as measurement light to the dispersion Lq, and is, for example, a He-Ne laser that emits laser light with a wavelength of 633 nm. The wavelength of the laser light is not particularly limited.

[0021] The first light source unit 20 and the second light source unit 22 emit laser light at different wavelengths. Note that the appropriate wavelength varies depending on the target particle being measured in the particle measuring device 10. Therefore, it is desirable to select a combination of wavelengths such that the refractive index difference between multiple particles differs significantly between wavelengths. Furthermore, the incident setting unit 12 sets at least one of the scattering angle and measurement wavelength as a measurement parameter. The measurement parameters include the scattering angle, the measurement wavelength, and combinations of the scattering angle and the measurement wavelength. In addition, the scattering angle may be set to two or more angles, or the measurement wavelength may be set to two or more wavelengths. Here, "2 angles" refers to the number of scattering angles. For example, 2 angles could be scattering angles of 45° and 90°. Furthermore, "two wavelengths" refers to the number of wavelengths being measured. For example, two wavelengths could be 633 nm and 488 nm.

[0022] The scattering angle can be changed, for example, by the rotating unit 36 ​​(described later) rotating the scattered light measurement unit 14 around the sample cell 16, and can be set to two or more angles. The parameter setting unit 13 is formed by the incident setting unit 12 and the rotating unit 36 ​​(described later). The parameter setting unit 13 sets at least one of the scattering angle and measurement wavelength as a measurement parameter, as described above. The measurement wavelength can be changed by switching between the first light source unit 20 and the second light source unit 22, allowing for two or more measurement wavelengths. For example, laser light with different wavelengths can be emitted from the first light source unit 20 and the second light source unit 22 as measurement light. Therefore, the configuration has a light source section corresponding to the number of measurement wavelengths, and is not limited to a first light source section 20 and a second light source section 22. If the measurement wavelength is not changed, one of the first light source section 20 and the second light source section 22 is sufficient. Furthermore, the number of light sources can be increased to increase the number of measurement wavelengths.

[0023] The sample cell 16 is, for example, a rectangular or cylindrical container made of optical glass or optical plastic. A dispersion Lq containing a single type of particle to be measured is placed in the sample cell 16. Laser light is shone onto the dispersion Lq as the measurement light. The sample cell 16 may be placed inside an immersion bath (not shown). The immersion bath is used to eliminate refractive index differences and to equalize the temperature.

[0024] As described above, the scattered light measurement unit 14 measures the scattering intensity of the scattered light generated when the laser light is scattered in the dispersion liquid Lq. The scattered light measurement unit 14 changes the values ​​of the measurement parameters set by the parameter setting unit 13 multiple times and measures the scattering intensity of the scattered light emitted from the dispersion Lq by the measurement light multiple times to obtain multiple scattering intensity data. Examples of multiple measurements of the scattering intensity of scattered light include measuring at multiple scattering angles and measuring at multiple measurement wavelengths. The scattered light measurement unit 14 includes a polarizing element 30 that transmits only a certain polarization component of the scattered light from the sample cell 16, a focusing lens 32 that images the scattered light onto the photodetector 34, and a photodetector 34 that detects the scattered light. Furthermore, a first pinhole (not shown) and a second pinhole (not shown) may be provided to appropriately set the scattering volume of the sample.

[0025] The polarizing element 30 can be appropriately selected to detect the polarization, such as circular polarization, linear polarization, or elliptic polarization. Alternatively, the polarizing element 30 may be configured with a polarizing element for detecting circular polarization and a polarizing element for detecting linear polarization side by side, and the light intensity of each polarization component of the scattered light may be detected by the photodetector 34 by switching between them according to the polarization to be detected. Furthermore, if it is not necessary to measure the light intensity of the polarization component of scattered light, the polarizing element 30 is not necessarily required.

[0026] The light detection unit 34 is not particularly limited as long as it can detect the intensity of scattered light; for example, a photomultiplier tube, photodiode, avalanche photodiode, time correlation meter, etc., can be used. Furthermore, the device has a rotating part 36 that rotates the scattered light measuring unit 14 to change the angle of the scattered light. The angle of the scattering angle θ can be changed by the rotating part 36. The angle of the scattering angle θ is the scattering angle. In Figure 1, the scattering angle is 90°. That is, the scattering angle is 90°. For example, a goniometer can be used as the rotating part 36. For example, the scattered light measuring unit 14 is placed on the goniometer which is the rotating part 36, and the scattering angle θ is adjusted by the goniometer.

[0027] As described above, the particle measuring device 10 has a first light source unit 20 and a second light source unit 22 that emit different laser light, enabling dynamic light scattering measurements using two or more measurement wavelengths, and allowing multiple scattering intensity data to be obtained for particles in the dispersion Lq. Furthermore, as described above, the particle measuring device 10 has a rotating part 36 that rotates the scattered light measuring unit 14, allowing dynamic light scattering measurements to be performed by changing the angle of the scattering angle θ, i.e., the value of the scattering angle, by two or more angles, and obtaining multiple scattering intensity data for particles in the dispersion Lq. The calculation unit 18 determines the refractive index and particle size distribution of particles in a dispersion Lq containing a single type of particle, based on the intensity of scattered light detected by the photodetector 34. The calculation unit 18 stores theoretical formulas that define the relationship between refractive index, particle size, and scattering intensity, as described later, and performs the fitting described later. In addition to determining the refractive index and particle size distribution of particles, the calculation unit 18 can also determine the number of particles.

[0028] The calculation unit 18 calculates time variation characteristic data of multiple scattering intensities of measurement parameters and parameter-dependent data of multiple scattering intensities of measurement parameters from multiple scattering intensity data obtained by the scattered light measurement unit 14. The calculation unit 18 then fits the calculated time variation characteristic data of multiple scattering intensities of measurement parameters and parameter-dependent data of multiple scattering intensities of measurement parameters with a theoretical formula that defines the relationship between refractive index, particle size, and scattering intensity, or with a simulation based on the theory of electromagnetic wave behavior, to determine the refractive index and particle size distribution of a single type of particle. The fitting process will be described later. In addition to theoretical formulas defining the relationship between refractive index, particle size, and scattering intensity, time-varying characteristic data of the scattering intensity of measurement parameters calculated by simulations based on the theory of electromagnetic wave behavior, and parameter-dependent data of the scattering intensity of the calculated measurement parameters may also be used.

[0029] In the calculation unit 18, the time variation characteristic data of the scattering intensity of the calculated measurement parameters is calculated based on the Stokes-Einstein theoretical formula. Furthermore, for example, parameter-dependent data of the scattering intensity is calculated based on at least one of the following: the Mie scattering theory formula, the discrete dipole approximation method (DDA method), and the finite difference time-domain method (FDTD method). Note that the discrete dipole approximation method (DDA method) and the finite difference time-domain method (FDTD method) correspond to simulations based on the theory of electromagnetic wave behavior. Any method equivalent to a simulation based on the theory of electromagnetic wave behavior can be used as appropriate, and the system is not particularly limited to the discrete dipole approximation method (DDA method) and the finite difference time-domain method (FDTD method) described above. Furthermore, the theoretical formulas are not limited to those mentioned above; various theoretical formulas, such as those from scattering theory, can be used as appropriate.

[0030] The calculation unit 18 determines the particle size distribution as described above by executing a program (computer software) stored in ROM (Read Only Memory) or the like on the calculation unit 18. The calculation unit 18 may be composed of a computer in which each part functions when the program is executed as described above, or it may be a dedicated device in which each part is composed of a dedicated circuit, or it may be composed of a server that runs on the cloud.

[0031] When measuring the scattering intensity of a dispersion, the scattering angle is used as a measurement parameter. If the scattering angle is the measurement parameter, the scattering intensity of the dispersion is measured for multiple scattering angles by changing the scattering angle value by two or more angles. In this case, for example, the measurement wavelength is fixed to one. If the measurement parameter is the measurement wavelength of the measurement light, the scattering intensity of the dispersion is measured at multiple measurement wavelengths using two or more measurement wavelengths. In this case, for example, the scattering angle is fixed to one value. The two wavelengths are the values ​​of the measurement parameter. The measurement parameters may also include the scattering angle and the measurement wavelength. In this case, the scattering angle is set to two or more angles, and the measurement wavelength is set to two or more wavelengths, and the scattering intensity of the dispersion is measured for each combination of scattering angle and measurement wavelength.

[0032] The scattering angle value is not particularly limited as long as it is 2 or more angles, but it is appropriately determined based on the number of scattering intensity data points, measurement time, etc. Preferably, the scattering angle value is greater than 0° and 180°. Furthermore, the measurement wavelength is not particularly limited as long as there are two or more wavelengths. The number of measurement wavelengths should be determined appropriately, taking into consideration factors such as the need for more light sources or optical elements to separate the wavelengths, which may increase as the number of measurement wavelengths increases. Furthermore, the measurement wavelength is not particularly limited, and light of various wavelengths such as ultraviolet light, visible light, and infrared light can be used as appropriate.

[0033] Furthermore, while scattering intensity can be measured using a single measuring device in conjunction with the dynamic light scattering measurement method or apparatus as described above, it may also be used in combination with measurement data from two different devices: a dynamic light scattering apparatus and a light scattering goniophotometer. For wavelength, a spectrometer may also be used. As described above, the apparatus configuration is not limited to, for example, the particle measurement apparatus 10 shown in Figure 1. The particles in the dispersion are of a single type. That is, assuming that there is only one type of particle in the dispersion, a theoretical formula is established that defines the relationship between refractive index, particle size, and scattering intensity, and the refractive index and particle size distribution of a single type of particle are determined.

[0034] (Example 1 of a particle measurement method) Figure 2 is a flowchart illustrating a first example of a particle measurement method according to an embodiment of the present invention. A first example of a particle measurement method involves using the scattering angle as the measurement parameter, and varying the scattering angle value by two or more angles to measure the scattering intensity of the dispersion at multiple scattering angles. The particle measurement method, as shown in Figure 2, includes, for example, a measurement step (step S10), a step of obtaining experimental data (step S12), and an optimization step (step S14). The optimization step (step S14) yields the analysis results (step S16), namely the refractive index (real part of the complex refractive index) and particle size distribution of a single type of particle (step S16). The particle size distribution is the distribution of the number of particles against the particle size, and is expressed in units of, for example, %. The measurement step (step S10) measures, for example, the time fluctuation of the scattering intensity and the scattering angle dependence of the time-averaged scattering intensity. The step of obtaining experimental data (step S12) involves obtaining, for example, an autocorrelation function for the time fluctuation of scattering intensity based on the measurements taken in the measurement step (step S10). It also involves obtaining the time-averaged scattering intensity dependent on the scattering angle or wavelength. This allows for obtaining, for example, the scattering intensity for each scattering angle shown in Figure 3.

[0035] In the optimization process (step S14), for example, the autocorrelation function and the theoretical formula for scattering intensity are fitted to the autocorrelation function of the time fluctuation of scattering intensity and the time-mean value of the scattering intensity obtained in step S12. In step S14, an initial value is set for the number of particles relative to the particle size of a single particle, and then the evaluation value is updated to minimize it to obtain the final number of particles. The initial value is set by generating a random variable. The following provides a more detailed explanation of the particle measurement method, including fitting.

[0036] First, a laser beam with a wavelength of, for example, 633 nm is irradiated onto the dispersion liquid Lq from the second light source unit 22 shown in Figure 1. The scattered light is detected by the photodetector unit 34 at a predetermined scattering angle for a predetermined time. This allows the scattering intensity of the dispersion liquid Lq at the scattering angle to be obtained. Next, the rotating unit 36 ​​rotates the scattered light measuring unit 14 to change the scattering angle θ and obtain the scattering intensity of the dispersion Lq. The scattering angle is changed and the scattering intensity of the dispersion Lq is measured repeatedly, and the scattering intensity of the dispersion Lq is measured multiple times. The scattering angle value is two or more angles, for example, the scattering intensity is measured every 5° from 30° to 160°. The above process constitutes the measurement process and corresponds to step S10 described above.

[0037] Next, the calculation unit 18 calculates the time variation characteristic data of the scattering intensity from the time dependence of the scattering intensity of the dispersion Lq obtained in the measurement step. The time variation characteristic data of the scattering intensity is either an autocorrelation function or a power spectrum. The autocorrelation function is calculated from the scattering intensity of the dispersion using a known method. The power spectrum is also calculated from the scattering intensity of the dispersion using a known method. In this way, time variation characteristic data of scattering intensity can be obtained for each scattering angle. In other words, there are multiple time variation data. Next, the calculation unit 18 calculates parameter-dependent data of the scattering intensity from the scattering intensity of the dispersion obtained in the measurement process. Parameter-dependent data of the scattering intensity of a dispersion can be obtained, for example, by calculating the time-averaged scattering intensity of the dispersion for each scattering angle. This yields scattering intensity data for each scattering angle, as shown in Figure 3. The calculation step involves calculating the time variation characteristic data of the scattering intensity of the dispersion and the parameter-dependent data of the scattering intensity of the dispersion, and corresponds to step S12 described above.

[0038] Next, the calculation unit 18 fits the time variation characteristic data of scattering intensity at at least one scattering angle and the parameter-dependent data of scattering intensity at multiple scattering angles using a theoretical formula that defines the relationship between refractive index, particle size, and scattering intensity, or a simulation based on the theory of electromagnetic wave behavior. This fitting determines the refractive index (real part of the complex refractive index) and particle size distribution of a single type of particle. This corresponds to steps S14 and S16 described above. As described above, the dispersion contains one type of particle. The first-order autocorrelation function is g (1) (τ) = exp(-Dq 2 τ). The relationship between the diffusion coefficient obtained from the autocorrelation function and the particle size is determined by applying the Stokes-Einstein formula used in the normal dynamic light scattering method.

[0039] When the particles have a particle size distribution, the first-order autocorrelation function is represented by the following formula (1). The scattering intensity is represented by the following formula (2). Formulas (1) and (2) are theoretical formulas, and the I in Formulas (1) and (2) <​​​​​​​​​​​​​​​​​​​​​​​​​​​​​ N d I d, θ / I θ total The part indicates the ratio of the scattering intensity by all single particles belonging to the bottle with particle size d to the total scattering intensity. The scattering intensity for a particle with particle size d and relative complex refractive index m is given by the following equation according to Mie scattering theory. The following equation is the theoretical formula that defines the relationship between refractive index, particle size, and scattering intensity.

[0043]

number

[0044] Here, P l is a function obtained by partially differentiating Legendre's polynomial with respect to θ, where the subscript l (L) represents the degree of Legendre's polynomial. λ refers to the wavelength in the solvent. d is the particle size, r is the distance from the particle, and m is the relative complex refractive index of the particle with respect to the medium. Note that when the refractive index of the solvent is n0 and the refractive index of the particle is n, m = n / n0. Furthermore, the coefficient A l (m, d) and B l (m, d) is given by the following equation. In the following equation, ' is the derivative with respect to the factors in each function.

[0045]

number

[0046]

number

[0047] x is defined by the following equation. Furthermore, ψ1(ρ) and ζ1(ρ) are expressed by the following equations, where J is the Bessel function and ζ is the Hankel function.

[0048]

number

[0049]

number

[0050]

number

[0051] <First example of fitting> The following describes the fitting process for determining the refractive index (real part of the complex refractive index) and particle size distribution of a single type of particle. In the fitting process, the number of particles is used as a variable to ultimately determine the refractive index (real part of the complex refractive index) and particle size distribution of a single type of particle. Second-order autocorrelation function g (2) (τ) is measured for each scattering angle, and two or more angles are preferable, but one angle is also acceptable. The number of scattering angles to be measured is determined appropriately according to the number of variables to be sought or the number of parameter-dependent data for the scattering intensity of the measurement parameters.

[0052] In the fitting process, for each scattering angle, the number of particles is used as a variable in equation (1) to set the initial number of particles. The calculated value of the first-order autocorrelation function in equation (1) is obtained based on the set initial number of particles. From the calculated value of the first-order autocorrelation function, the second-order autocorrelation function g is obtained. (2) (τ) = 1 + β·|g (1) (τ)| 2 Calculate the value of β. Note that β is the device constant. For each scattering angle, the difference between the measured value of the second-order autocorrelation function and the calculated value of the second-order autocorrelation function is calculated. This difference between the measured value and the calculated value of the second-order autocorrelation function is called the difference in the second-order autocorrelation function. The difference in the second-order autocorrelation function is obtained for each scattering angle. The calculated value of the second-order autocorrelation function for each scattering angle corresponds to the time variation characteristic data of the scattering intensity of the measured parameter calculated using the theoretical formula.

[0053] Total scattering intensity I totalThis has been measured for each scattering angle. In equation (2), the total scattering intensity I of equation (2) is based on the set initial number of particles. θ total Find the value of this. For each scattering angle, the measured total scattering intensity I is as shown in Figure 3. total The value of and the total scattering intensity I in equation (2) θ total The difference between this value and the calculated value is calculated. Note that the measured total scattering intensity I at any scattering angle is calculated. total The value of and the total scattering intensity I in equation (2) θ total The difference from the calculated value is the total scattering intensity I at the scattering angle. total This is called the difference in total scattering intensity I total Regarding the total scattering intensity I at the scattering angle, total The difference is obtained. Total scattering intensity I in equation (2) θ total The calculated value corresponds to the parameter-dependent data of the scattering intensity of the measurement parameters calculated by the theoretical formula. However, when calculating the second-order autocorrelation function using equation (1) and when calculating the total scattering intensity using equation (2), d (particle size in dynamic light scattering, d) in equation (1) DLS (Assuming) and (2) d (particle size in static light scattering, d SLS The ratio α = d SLS / d DLS For example, this could be set to 0.78. However, α is a coefficient determined by the particle structure.

[0054] In the fitting process, the difference between the second-order autocorrelation functions obtained for each scattering angle and the difference in total scattering intensity at each scattering angle are used to determine the final particle number and refractive index (real part of the complex refractive index). For example, an evaluation value is obtained by summing the square of the difference between the second-order autocorrelation functions obtained for each scattering angle and the square of the difference in total scattering intensity at each scattering angle for all scattering angles. The particle number that minimizes this evaluation value is taken as the final particle number. Therefore, in the fitting process, the number of particles and the relative complex refractive index m are repeatedly updated in equations (1) and (2) to minimize the evaluation value, thereby obtaining the final number of particles and relative complex refractive index m. Then, assuming that the type of solvent, i.e., the refractive index, is known, the refractive index n of the particles is obtained from the relative complex refractive index m. The refractive index n of the particles obtained from the relative complex refractive index m is the real part of the complex refractive index.

[0055] In the fitting process, the values ​​of the number of particles and the relative complex refractive index m are updated in equations (1) and (2) above, reflecting the equations showing the relative complex refractive index m described above. A fitting is then performed between the measured and calculated values ​​to obtain the final number of particles and the relative complex refractive index m. The refractive index is fitted through the equations showing the relative complex refractive index m described above. After setting initial values ​​for the number of particles for all particle sizes, the evaluation value is updated to minimize it. This allows us to obtain a particle histogram. That is, N d c For all d=d0~d M By determining this, the particle size distribution can be obtained. This corresponds to step S16 described above.

[0056] The above steps constitute the process of determining the particle size distribution of a single type of particle (step S16). Note that the evaluation values ​​used for fitting are not limited to those described above. Furthermore, the methods for optimizing the fitting are not limited to those described above; for example, Bayesian optimization can be used for fitting. Furthermore, while a second-order autocorrelation function was used, it is not limited to this; a power spectrum can also be used instead. Additionally, if a first-order autocorrelation function is measured experimentally using heterodyne detection, a first-order autocorrelation function may be used instead.

[0057] Here, Figure 3 is a graph showing an example of the relationship between scattering intensity and scattering angle for an aqueous dispersion of polystyrene particles with a particle size of 990 nm. Figure 4 is a graph showing an example of the second-order autocorrelation function for each scattering angle, and shows the scattering angle dependence of the second-order autocorrelation function for an aqueous dispersion of polystyrene particles with a particle size of 990 nm. In Figure 4, the symbol 37 represents the second-order autocorrelation function at a scattering angle of 50°. The symbol 38 represents the second-order autocorrelation function at a scattering angle of 90°. The symbol 39 represents the second-order autocorrelation function at a scattering angle of 140°. Figure 5 is a graph showing the calculated scattering angle and scattering intensity for particles of the same particle size, for each refractive index, and shows the scattering intensity profile obtained by calculation. In Figure 5, reference numeral 40 represents the profile showing the relationship between scattering angles for a refractive index of 1.48. Reference numeral 41 represents the profile showing the relationship between scattering angles for a refractive index of 1.59. Reference numeral 42 represents the profile showing the relationship between scattering angles for a refractive index of 2.2. As shown in Figure 5, even for particles of the same particle size, if the refractive index is different, the scattering intensity profile with respect to scattering angle will be different.

[0058] The above fitting yields the refractive index n=1.59 and particle size d=990nm for polystyrene. The refractive index n=1.59 is the real part of the complex refractive index. The refractive index and particle size of polystyrene are determined as described in the fitting procedure above. In accordance with the formula for the relative complex refractive index m described above, the values ​​of the particle number and relative complex refractive index m are updated in equations (1) and (2) above, and a fitting is performed between the measured and calculated values. The refractive index is fitted through the formula for the relative complex refractive index m described above. In this way, the final particle number and relative complex refractive index m are obtained. The particle size distribution is then obtained based on the final particle number and particle size.

[0059] In addition to the scattering angle, results measured at different wavelengths can also be added to determine the wavelength dependence of the refractive index. That is, by using two or more measurement wavelengths and measuring the scattered light intensity at each of the multiple measurement wavelengths, multiple scattered light data can be obtained to determine the number of particle species, the refractive index of each particle species, and the particle size distribution. In this case, the scattering angle can be one angle, or multiple angles, including two or more angles. By changing the measurement wavelength, the wavelength dependence of the refractive index can be obtained. This wavelength dependence of the refractive index is also called refractive index dispersion. When changing the measurement wavelength as a measurement parameter, the measurement wavelength is not limited to two; it can be three, four, or any other wavelength.

[0060] Here, Figures 6 and 7 show the relationship between scattering intensity and measurement wavelength. Figure 6 shows the scattering intensity calculated for two types of particles with different refractive indices at a measurement wavelength of 488 nm. As shown in Figure 6, the scattering intensity profile 44 of the first particle and the scattering intensity profile 45 of the second particle are different. Figure 7 shows the scattering intensities of two types of particles calculated at a measurement wavelength of 632.8 nm. As shown in Figure 7, the scattering intensity profile 46 of the first particle and the scattering intensity profile 47 of the second particle are different. As shown in Figures 6 and 7, the scattering intensity with respect to the measurement wavelength differs due to the difference in refractive index of the particles. For example, parameter-dependent data of the scattering intensity of a dispersion can be obtained by calculating the time-averaged scattering intensity of the dispersion for each laser light wavelength. In addition to the scattering angle, increasing the number of wavelengths measured allows us to obtain information about the wavelength dependence of the refractive index. In this case, we can use the formula for the wavelength dependence of the refractive index N, for example, Cauchy's formula, N = D1 + D2 / λ. 2 The refractive index N can also be obtained by similarly determining the values ​​D1 and D2 using the same method.

[0061] By using formulas determined by empirical or physical laws, it is possible to reduce the number of parameters required for fitting and thus the computational complexity of fitting when increasing the number of measurement wavelengths. This can shorten the time required for fitting. In addition to theoretical formulas, fitting can also utilize time-varying data of the scattering intensity of the measured parameters calculated through simulation, as well as parameter-dependent data of the scattering intensity of the calculated measured parameters.

[0062] In the measurement process, the light intensity of the polarization component of the scattered light of the dispersion obtained by irradiating the dispersion with measurement light of a specific polarization may be measured as the scattering intensity. This measurement process is performed by the scattered light measurement unit 14. For example, circularly polarized laser light is shone onto the dispersion Lq of sample cell 16 as the measurement light, and the polarization component of the scattered light of the dispersion Lq is measured. For example, the light intensity of the polarization component of the scattered light is measured as the difference between the light intensity of vertically linearly polarized light and the light intensity of horizontally linearly polarized light. In this case, as in the first example of the particle measurement method described above, if the scattering angle is changed during measurement, a graph showing the relationship between scattering intensity and scattering angle, as shown in Figure 8, can be obtained. As shown in Figure 8, the scattering intensity profile 48 for spherical particles and the scattering intensity profile 49 for disc-shaped particles are different. Furthermore, perpendicular linear polarization refers to the direction of linear polarization being perpendicular when the scattering surface is considered horizontal. Horizontal linear polarization refers to the direction of linear polarization being horizontal when the scattering surface is considered horizontal.

[0063] Furthermore, the measurement process may involve measuring at least one of the following: parameter-dependent data of scattering intensity obtained by sequentially irradiating the dispersion with measurement light in multiple polarization states, and parameter-dependent data of scattering intensity obtained by extracting multiple polarization components of scattered light emitted from the dispersion. This measurement process is performed by the scattered light measurement unit 14 and the polarizing element 28. The parameter-dependent scattering intensity data obtained by sequentially irradiating a dispersion with measurement light in multiple polarization states is based on the assumption that the measurement light is in a polarized state. Furthermore, the parameter-dependent scattering intensity data obtained by extracting multiple polarization components of scattered light emitted from the dispersion is based on detecting the polarization components of scattered light without considering the measurement light as polarized. The data obtained by considering the measurement light as polarized and detecting the polarization components of scattered light is also included in the aforementioned parameter-dependent scattering intensity data. For example, when using polarization, the polarization state of the measured light can be set to circular polarization, and the polarization component of the scattered light can be the difference between the vertical polarization intensity and the horizontal polarization intensity. Alternatively, for example, the polarization state of the measured light can be set to 45° linear polarization, and the polarization component of the scattered light can be the sum of the vertical polarization intensity and the horizontal polarization intensity.

[0064] (Second example of a particle measuring device) Figure 9 is a schematic diagram showing a second example of a particle measuring device according to an embodiment of the present invention. In the particle measuring device 60 shown in Figure 9, the same components as those in the particle measuring device 10 shown in Figure 1 are given the same reference numerals, and their detailed descriptions are omitted. The particle measuring device 60 shown in Figure 9 differs from the particle measuring device 10 shown in Figure 1 in that it uses a white light source and the arrangement of optical elements are different.

[0065] The particle measuring device 60 includes a light source unit 62, a beam splitter 64, a lens 65, and a sample cell 16. The light source unit 62, the beam splitter 64, the lens 65, and the sample cell 16 are arranged in series on a straight line L1. The light source unit 62 emits incident light Ls, and a white light source is used. For example, a supercontinium (SC) light source is used as the white light source. Lens 65 is an objective lens that focuses the incident light Ls onto the sample cell 16. The beam splitter 64 has a transmissive reflective surface 64a that transmits light incident from one direction and reflects light incident from the other direction. The beam splitter 64 is a cube-shaped beam splitter.

[0066] In the beam splitter 64, the first axis C is perpendicular to the aforementioned straight line L1. 11 At the top, the shutter 66, lens 67, pinhole 68, lens 69, and beam splitter 70 are arranged in series. The beam splitter 70 has a transmissive reflective surface 70a that transmits light incident from one direction and reflects light incident from the other direction. The beam splitter 70 is a cube-shaped beam splitter. Opposite the surface 70b where the lens 69 of the beam splitter 70 is not located, the slit 71 and the mirror 72 are aligned along the first axis C 11 They are arranged in series on top of each other. The opening 71a of the slit 71 is open to the surface 70b. Light passing through the opening 71a of the slit 71 is incident on the mirror 72. The system further includes a diffraction grating 73 to which the reflected light reflected by the mirror 72 is incident.

[0067] The diffraction grating 73 is an optical element that wavelength-decomposes incident light, including scattered light, into light of each wavelength. By using the diffraction grating 73, scattered light of each wavelength can be obtained. Furthermore, it has a photodetector 74 into which diffracted light, which has been diffracted according to its wavelength by a diffraction grating 73, is incident. The photodetector 74 detects the wavelength-decomposed scattered light for each wavelength. The photodetector 74 is connected to the calculation unit 18. The photodetector 74 has multiple pixels and detects the average time intensity and time dependence of the light intensity of each pixel. For example, a line camera with photoelectric conversion elements arranged in a straight line can be used as the photodetector 74. Alternatively, the photodetector 74 may be a system in which photomultiplier tubes are arranged in a straight line instead of a line camera. The spectroscopic detection unit 80 is composed of a mirror 72, a diffraction grating 73, and a photodetector 74.

[0068] For sample cell 16, the first axis C 11 A second axis C parallel to the first axis 12 At the top, the shutter 75, lens 76, pinhole 77, lens 78, and mirror 79 are arranged in series. The light reflected by the mirror 79 enters the surface 70c of the beam splitter 70 and is reflected toward the mirror 72 by the transmissive reflective surface 70a of the beam splitter 70. For example, electromagnetic shutters are used for shutters 66 and 75. Shutters 66 and 75 control the incidence of light to the beam splitter 70. By switching the opening and closing of shutters 66 and 75, either of the light reflected by the sample cell 16 can be directed to the beam splitter 70. When measuring both of the light reflected by the sample cell 16, shutters 66 and 75 are switched sequentially during measurement. Pinholes 68 and 77 have a confocal function, allowing only the component of light scattered at the focal point of the dispersion Lq to pass through the pinholes. This limits the measurement area of ​​the scattered light from the dispersion Lq, enabling measurements without degrading spatial coherence.

[0069] In the particle measuring device 60, for example, a supercontinuum light source is used in the light source unit 62. Light from the light source unit 62 is irradiated onto the sample cell 16 via the beam splitter 64 and lens 65. In the sample cell 16, the backscattered light with a scattering angle of 180° returns to the beam splitter 64, enters the beam splitter 64 from the surface 64c of the beam splitter 64, is reflected by the transmission reflection surface 64a, and then passes through lens 67, pinhole 68 and lens 69. At this time, shutter 66 is open and shutter 75 is closed. As described above, the pinhole 68 has a confocal function, and only the component of light scattered at the focal point of the dispersion Lq can pass through the pinhole 68. This limits the measurement area of ​​the scattered light of the sample cell 16, allowing the scattered light to be measured without degrading spatial coherence. Subsequently, the scattered light passes through the beam splitter 70, through the slit 71, is reflected by the mirror 72 in the spectroscopic detection unit 80, enters the diffraction grating 73, and then reaches the photodetector 74, where it is detected by the photodetector 74. The diffraction grating 73 irradiates the scattered light onto different pixels for each wavelength, and the scattered light is detected spectrally. That is, the scattered light is detected for each wavelength.

[0070] On the other hand, when measuring scattered light reflected at 90° from the sample cell 16, it passes through lens 76, pinhole 77, and lens 78. At this time, shutter 75 is open and shutter 66 is closed. At mirror 79, the scattered light is reflected by beam splitter 70, reflected by the transmission reflective surface 70a of beam splitter 70, passes through slit 71, is reflected by mirror 72 in the spectroscopic detection unit 80, enters diffraction grating 73, and the scattered light that reaches photodetector 74 is detected by photodetector 74. In this way, the particle measuring device 60 measures the intensity of scattered light at different scattering angles for each wavelength. Similar to the particle measuring device 10, the particle measuring device 60 can measure the refractive index and particle size distribution of a single type of particle contained in the dispersion.

[0071] In the calculation unit 18, it is preferable to compare the refractive index of a single type of particle, obtained by the fitting described above, with the refractive index when the known material is at 100% concentration, i.e., the refractive index of the known material in bulk state, and to calculate the volume concentration of the constituent material of the single type of particle using the dependence of the refractive index on the particle volume concentration. Note that volume concentration is synonymous with volume density and packing efficiency. Furthermore, the dependence of the refractive index means, for example, that the refractive index changes linearly with respect to the volume density. In the particle measurement method, it is preferable to include a step of comparing the refractive index of a single type of particle obtained with the refractive index of a known material at 100% concentration, and using the dependence of the refractive index on the particle volume concentration to calculate the volume concentration of the constituent material of the single type of particle obtained. This allows, for example, the density of an aggregate to be estimated from the refractive index of the single type of particle obtained. Furthermore, for known materials at 100% concentration, the refractive index of the material and its refractive index at 100% concentration are associated and stored in the calculation unit 18 as a library, for example.

[0072] (Third example of a particle measuring device) Figure 10 is a schematic diagram showing a third example of a particle measuring device according to an embodiment of the present invention. In the particle measuring device 10a shown in Figure 10, the same components as those in the particle measuring device 10 shown in Figure 1 are given the same reference numerals, and their detailed descriptions are omitted. The particle measuring device 10a shown in Figure 10 differs from the particle measuring device 10 shown in Figure 1 in that it measures the transmittance of the dispersion Lq, and has a transmitted light measuring unit 90 for measuring transmittance. The transmitted light measuring unit 90 is connected to the calculation unit 18. For example, a photomultiplier tube or a photodiode can be used in the transmitted light measuring unit 90.

[0073] The particle measuring device 10a has a transmitted light measuring unit 90 that faces the polarizing element 28 with the sample cell 16 in between, and is positioned on the optical axis C1. The transmitted light measuring unit 90 measures the light intensity of the transmitted light that has passed through the sample cell 16, and is not particularly limited to a photomultiplier tube as long as it can measure the light intensity of the transmitted light. The light intensity of the transmitted light obtained by the transmitted light measuring unit 90 is output to the calculation unit 18. The calculation unit 18 calculates the transmittance of the dispersion Lq and obtains the transmittance data of the dispersion Lq. The calculation unit 18 and the transmitted light measuring unit 90 constitute a transmittance measuring unit, and the transmittance of the dispersion Lq is measured by the transmittance measuring unit. The light intensity of the light incident on the sample cell 16 is 1 i The light intensity of the transmitted light that passed through the sample cell 16 is set to I o In this case, the transmittance Ts is I o / I i Furthermore, the transmittance Ts is expressed by the following equation (3).

[0074] Ts=exp(-τ a L) (3) In equation (3) for transmittance Ts, τ a τ is the absorption coefficient, and L is the optical path length. a This is expressed by the following equation (4). In the following equation (4), N is the number of particles (the subscript d indicates that it depends on the particle size diameter d). C ext Here, the extinction cross-section (where d is the particle diameter and m is the relative complex refractive index of the particle with respect to the refractive index n0 of the solvent (m=n)) is given by... c n0): n is the complex refractive index of the particle. cLet =n+ik. The subscripts 0 to M for d are the ordinal numbers of the bins in the particle histogram shown in Figure 11.

[0075]

number

[0076] Note that the extinction cross-sectional area C ext The extinction cross-sectional area C is expressed by the following formula: ext a of the expression n , b n It is expressed by the following formula. Also, Ψ n (ρ) and ζ n (ρ) is expressed by the following formula.

[0077]

number

[0078]

number

[0079]

number

[0080]

number

[0081]

number

[0082]

number

[0083] In the above equation, Ψ n (ρ) and ζ n (ρ) is the Riccati-Bessel function.n (ρ) is the first kind of spherical Bessel function, and h n (2) (ρ) is the second kind of sphere Hankel function, and λ is the wavelength.

[0084] The calculation unit 18 of the particle measuring device 10a calculates time variation characteristic data of multiple scattering intensities of measurement parameters and parameter-dependent data of multiple scattering intensities of measurement parameters from multiple scattering intensity data obtained by the scattered light measuring unit 14. The calculation unit 18 then fits the calculated time variation characteristic data of multiple scattering intensities of measurement parameters and parameter-dependent data of multiple scattering intensities of measurement parameters, along with the transmittance data of the dispersion, using a theoretical formula defining the relationship between complex refractive index, particle size, and scattering intensity, or a simulation based on the theory of electromagnetic wave behavior, and a theoretical formula defining the relationship between complex refractive index, particle size, and transmittance, or a simulation based on the theory of electromagnetic wave behavior, to determine the complex refractive index and particle size distribution of a single type of particle. The fitting will be described later. In addition to theoretical formulas defining the relationship between complex refractive index, particle size, and scattering intensity, and theoretical formulas defining the relationship between complex refractive index, particle size, and transmittance, time variation characteristic data of the scattering intensity of measurement parameters, parameter-dependent data of the calculated scattering intensity of measurement parameters, and transmittance data may also be used, calculated by simulation based on the theory of electromagnetic wave behavior.

[0085] In the calculation unit 18, the time variation characteristic data of the scattering intensity of the calculated measurement parameters is calculated based on the Stokes-Einstein theoretical formula. Furthermore, for example, parameter-dependent data of the scattering intensity is calculated based on at least one of the following: the Mie scattering theory formula, the discrete dipole approximation method (DDA method), and the finite difference time-domain method (FDTD method). Note that the discrete dipole approximation method (DDA method) and the finite difference time-domain method (FDTD method) correspond to simulations based on the theory of electromagnetic wave behavior. Any method equivalent to a simulation based on the theory of electromagnetic wave behavior can be used as appropriate, and the system is not particularly limited to the discrete dipole approximation method (DDA method) and the finite difference time-domain method (FDTD method) described above. Furthermore, the theoretical formulas are not limited to those mentioned above; various theoretical formulas, such as those from scattering theory, can be used as appropriate. Furthermore, simulations based on the theory of electromagnetic wave behavior relating to complex refractive index, particle size, and transmittance can utilize, for example, the Mie scattering theory equation, the discrete dipole approximation method (DDA method), and the finite difference time-domain method (FDTD method), similar to simulations based on the theory of electromagnetic wave behavior relating to complex refractive index, particle size, and scattering intensity.

[0086] Furthermore, the transmittance of the dispersion Lq is not limited to being measured with the particle measuring device 10a; the transmittance of the dispersion Lq measured in advance may also be used. Therefore, the particle measuring device 10 shown in Figure 1 can also determine the complex refractive index in the same way as the particle measuring device 10a.

[0087] (Second example of a particle measurement method) Figure 12 is a flowchart illustrating a second example of a particle measurement method according to an embodiment of the present invention. The second example of the particle measurement method differs from the first example in that it uses the scattering intensity of the dispersion to determine the complex refractive index. The second example of the particle measurement method differs from the first example in that it uses the transmittance of the dispersion and determines the complex refractive index, which consists of a real part and an imaginary part. The transmittance of the dispersion may be measured before or after measuring the scattering intensity of the dispersion to be measured. Also, if the transmittance of the dispersion is known, that known transmittance can be used. As shown in Figure 12, the particle measurement method includes, for example, a measurement step (step S20), a step of obtaining experimental data (step S22), and an optimization step (step S24). The optimization step (step S24) yields the analysis results (step S26), namely the complex refractive index and particle size distribution of a single type of particle (step S26). The measurement process (step S20) measures, for example, the time fluctuation of the scattering intensity, the scattering angle dependence of the time-averaged scattering intensity, and the transmittance of the dispersion.

[0088] The step of obtaining experimental data (step S22) involves obtaining, for example, an autocorrelation function with respect to the time fluctuation of scattering intensity based on the measurements taken in the measurement step (step S20). It also involves obtaining the time-averaged scattering intensity dependent on the scattering angle or wavelength. Furthermore, the transmittance of the dispersion is measured to obtain transmittance data. This allows for obtaining, for example, the scattering intensity for each scattering angle shown in Figure 3. Additionally, the transmittance of the dispersion is obtained. Note that the transmittance data may be obtained during the measurement step (step S20) described above. However, since transmittance data is only necessary during fitting, the step of obtaining transmittance data can be performed before fitting, that is, before the step of determining the complex refractive index and particle size distribution of a single type of particle. Also, if the transmittance data is known, the known transmittance data can be used, so the step of obtaining transmittance data is not necessarily required.

[0089] In the optimization step (step S24), for example, the autocorrelation function, scattering intensity, and theoretical formulas for the dispersion's transmittance are fitted to the autocorrelation function of the time fluctuation of the scattering intensity, the time-averaged value of the scattering intensity, and the transmittance of the dispersion obtained in step S22. In step S24, an initial value is set for the number of particles relative to the particle size of a single particle, and then the evaluation value is updated to minimize it to obtain the final number of particles. The initial value is set by generating a random variable. The following provides a more detailed explanation of the particle measurement method, including fitting.

[0090] First, a laser beam with a wavelength of, for example, 488 nm is irradiated onto the dispersion liquid Lq from the second light source unit 22 shown in Figure 10. The scattered light is detected by the photodetector unit 34 at a predetermined scattering angle for a predetermined time. This allows the scattering intensity of the dispersion liquid Lq at the scattering angle to be obtained. In addition, the transmitted light that has passed through the dispersion liquid Lq is also measured in light intensity by the transmitted light measurement unit 90. Next, the scattered light measuring unit 14 is rotated by the rotating unit 36 ​​to change the scattering angle θ and obtain the scattering intensity of the dispersion Lq. The scattering angle is changed and the scattering intensity of the dispersion Lq is measured repeatedly, and the scattering intensity of the dispersion Lq is measured multiple times. The scattering angle value is two or more angles, for example, the scattering intensity is measured every 5° from 30° to 160°. The above process constitutes the measurement process and corresponds to step S20 described above.

[0091] Next, the calculation unit 18 calculates the time variation characteristic data of the scattering intensity from the time dependence of the scattering intensity of the dispersion Lq obtained in the measurement step. The time variation characteristic data of the scattering intensity is either an autocorrelation function or a power spectrum. The autocorrelation function is calculated from the scattering intensity of the dispersion using a known method. The power spectrum is also calculated from the scattering intensity of the dispersion using a known method. In this way, time variation characteristic data of scattering intensity can be obtained for each scattering angle. In other words, there are multiple time variation data. Furthermore, the calculation unit 18 calculates the transmittance of the dispersion Lq from the light intensity of the laser light and the light intensity of the transmitted light that has passed through the dispersion Lq using the above formula. Note that if the wavelength of the laser light is changed, the transmittance can be obtained for each wavelength of the laser light. In other words, wavelength-dependent data of the transmittance can be obtained.

[0092] Next, the calculation unit 18 calculates parameter-dependent data of the scattering intensity from the scattering intensity of the dispersion obtained in the measurement process. Parameter-dependent data of the scattering intensity of a dispersion can be obtained, for example, by calculating the time-averaged scattering intensity of the dispersion for each scattering angle. This yields scattering intensity data for each scattering angle, as shown in Figure 3. The calculation process involves calculating the time variation characteristic data of the scattering intensity of the dispersion, the parameter-dependent data of the scattering intensity of the dispersion, and the transmittance of the dispersion Lq, and corresponds to step S22 described above.

[0093] Next, in the calculation unit 18, time variation characteristic data of scattering intensity at at least one scattering angle, parameter-dependent data of scattering intensity at multiple scattering angles, and transmittance data of the dispersion are fitted using a theoretical formula defining the relationship between complex refractive index, particle size, and scattering intensity, or a simulation based on the theory of electromagnetic wave behavior, and a theoretical formula defining the relationship between complex refractive index, particle size, and transmittance, or a simulation based on the theory of electromagnetic wave behavior. This fitting determines the complex refractive index and particle size distribution of a single type of particle. This corresponds to steps S24 and S26 described above. The theoretical formula defining the relationship between complex refractive index, particle size, and transmittance is, for example, the absorption coefficient τ in equation (4) described above. a This is the formula. As mentioned above, the dispersion contains one type of particle. The first-order autocorrelation function is, as mentioned above, g (1) (τ) = exp(-Dq) 2 It is expressed as τ). The relationship between the diffusion coefficient obtained from the autocorrelation function and the particle size is determined by applying the Stokes-Einstein formula, which is commonly used in dynamic light scattering.

[0094] If the particles have a particle size distribution, the first-order autocorrelation function is given by equation (1) above. The scattering intensity is given by equation (2) above. Equations (1) and (2) above are theoretical formulas, and the I of equations (1) and (2) θ total These are all calculated values.

[0095] <Second example of fitting> The following describes the fitting process for determining the complex refractive index and particle size distribution of a single type of particle. In the fitting process, the number of particles is used as a variable to ultimately determine the complex refractive index and particle size distribution of a single type of particle. Second-order autocorrelation function g (2) (τ) is measured for each scattering angle, and two or more angles are preferable, but one angle is also acceptable. The number of scattering angles to be measured is determined appropriately according to the number of variables to be sought or the number of parameter-dependent data for the scattering intensity of the measurement parameters.

[0096] In fitting, for the first-order autocorrelation function for each scattering angle, in Equation (1) respectively, with the number of particles as a variable, the initial number of particles is set. Based on the set initial number of particles, the calculated value of the first-order autocorrelation function in Equation (1) is obtained. From the calculated value of the first-order autocorrelation function, the second-order autocorrelation function g (2) (τ)=1 + β·|g (1) (τ)| 2 of the calculated value is obtained. Here, β is a device constant. For each scattering angle, the difference between the measured value of the second-order autocorrelation function and the calculated value of the second-order autocorrelation function is obtained. Here, the difference between the measured value of the second-order autocorrelation function and the calculated value of the second-order autocorrelation function is referred to as the difference of the second-order autocorrelation function. The difference of the second-order autocorrelation function is obtained for each scattering angle. The calculated value of the second-order autocorrelation function for each scattering angle corresponds to the time-varying characteristic data of the scattering intensity of the measurement parameters calculated by the theoretical formula.

[0097] The total scattering intensity I total has been measured for each scattering angle. In Equation (2), based on the set initial number of particles, the value of the total scattering intensity I θ total in Equation (2) is obtained. For each scattering angle, the measured value of the total scattering intensity I total as shown in FIG. 3 and the calculated value of the total scattering intensity I θ total in Equation (2) are obtained. Here, the measured value of the total scattering intensity I total at an arbitrary scattering angle and the calculated value of the total scattering intensity I θ total in Equation (2) is referred to as the difference in the total scattering intensity I total at the scattering angle. For the total scattering intensity I total , the difference in the total scattering intensity I total at the scattering angle is obtained. The calculated value of the total scattering intensity I θ total in Equation (2) corresponds to the parameter-dependent data of the scattering intensity of the measurement parameters calculated by the theoretical formula. The measured value of the transmittance and Ts = exp(-τ aFind the difference from the calculated value of the transmittance Ts of (L). Note that the difference between the measured transmittance value and the calculated value of the transmittance Ts is referred to as the transmittance difference.

[0098] In fitting, in order to obtain the final number of particles and the refractive index, the difference in the second-order autocorrelation function obtained for each of the above scattering angles, the difference in the total scattering intensity at the scattering angle, and the transmittance difference are used. For example, the sum of the squared values of the differences in the second-order autocorrelation function obtained for each scattering angle and the squared value of the difference in the total scattering intensity at the scattering angle for all scattering angles, and the squared value of the transmittance difference are added to obtain an evaluation value. The number of particles at which the evaluation value is minimized is taken as the final number of particles. Therefore, in fitting, the number of particles and the relative complex refractive index m are repeatedly updated in equations (1), (2) and equation (4) so that the evaluation value is minimized, and the final number of particles and the relative complex refractive index m are obtained. Then, assuming that the type of solvent, that is, the refractive index is known, the refractive index n of the particles is obtained from the relative complex refractive index m.

[0099] In fitting, reflecting the above equation showing the relative complex refractive index m, in the above equations (1), (2) and equation (4), the values of the number of particles and the relative complex refractive index m are updated, and fitting of the measured value and the calculated value is performed to obtain the final number of particles and the relative complex refractive index m. The complex refractive index is fitted through the above equation showing the relative complex refractive index m. After setting an initial value for the number of particles for all particle sizes, update so as to minimize the evaluation value. Thereby, a histogram of the particles can be obtained. That is, N d c for all d = d0 to d M is obtained to obtain the particle size distribution. This corresponds to the above step S26.

[0100] The above process is the process (step S26) of obtaining the particle size distribution of a single type of particle. Note that the evaluation value used in fitting is not limited to the above. Furthermore, the methods for optimizing the fitting are not limited to those described above; for example, Bayesian optimization can be used for fitting. Furthermore, while a second-order autocorrelation function was used, it is not limited to this; a power spectrum can also be used instead. Additionally, if a first-order autocorrelation function is measured experimentally using heterodyne detection, a first-order autocorrelation function may be used instead.

[0101] In addition to the scattering angle, results measured at different wavelengths can also be added to determine the wavelength dependence of the complex refractive index. That is, multiple scattered light intensity is measured at multiple measurement wavelengths (two or more) to obtain data for multiple scattered light wavelengths. Alternatively, transmittance can be measured at multiple measurement wavelengths (two or more) to obtain transmittance for each measurement wavelength. The number of particle species, the complex refractive index for each particle species, and the particle size distribution can also be determined. In this case, the scattering angle may be one angle, multiple angles, or two or more angles. By changing the measurement wavelength, the wavelength dependence of the complex refractive index can be obtained. This wavelength dependence of the complex refractive index is also called refractive index dispersion. When changing the measurement wavelength as a measurement parameter, the measurement wavelength is not limited to two; it can be three, four, or any other wavelength.

[0102] Furthermore, the volume concentration of the dispersion can be used for fitting. In this case, the calculation unit 18 can determine the complex refractive index of a single type of particle and the particle size distribution of the number concentration by fitting the scattering intensity time variation characteristic data, the scattering intensity parameter dependence data, the transmittance data, and the dispersion volume concentration data. Here, the dispersion volume concentration data is data indicating the volume concentration of the dispersion, and the volume concentration φ is expressed by the following formula. In the following formula for volume concentration φ, d is the particle size. Furthermore, the particle size distribution of the number concentration refers to the distribution of the number of particles per unit volume of the dispersion relative to the particle size. d This represents the number of particles per unit volume of the dispersion.

[0103]

number

[0104] When the volume concentration of a dispersion is known, the difference between the measured volume concentration and the calculated volume concentration φ, expressed by the following formula, is determined. The difference between the measured volume concentration and the calculated volume concentration φ is called the difference in volume concentration. The known volume concentration value is, for example, a measured value. One method for determining the volume concentration of a dispersion is to centrifuge the particles in the dispersion to settle them, measure the particle weight, calculate the weight of the dispersion medium, and then determine the volume concentration of the dispersion from the known specific gravities of the particles and the dispersion medium. In the fitting process, to determine the final particle number and complex refractive index, the difference in the second-order autocorrelation function obtained for each scattering angle, the difference in total scattering intensity at each scattering angle, the difference in transmittance, and the difference in volume concentration are used. For example, an evaluation value is obtained by adding the squared difference in the second-order autocorrelation function obtained for each scattering angle, the squared difference in total scattering intensity at each scattering angle, the squared difference in transmittance, and the squared difference in volume concentration for all scattering angles. The particle number that minimizes this evaluation value is taken as the final particle number. At this point, the particle number is obtained as the number concentration. This allows the absolute number of particles in the dispersion to be obtained.

[0105] (Fourth example of a particle measuring device) Figure 13 is a schematic diagram showing a fourth example of a particle measuring device according to an embodiment of the present invention. In the particle measuring device 60a shown in Figure 13, the same components as those in the particle measuring device 60 shown in Figure 9 are given the same reference numerals, and their detailed descriptions are omitted. The particle measuring device 60a shown in Figure 13 differs from the particle measuring device 60 shown in Figure 9 in that it measures the transmittance of the dispersion Lq, and has a transmitted light measuring unit 90 for measuring transmittance. The transmitted light measuring unit 90 is positioned opposite the lens 65 with the sample cell 16 in between.

[0106] The transmitted light measuring unit 90 is connected to the calculation unit 18, although it is not shown in the figure. Similar to the particle measuring device 10a shown in Figure 10, the transmittance measuring unit is composed of the calculation unit 18 and the transmitted light measuring unit 90. The transmittance measuring unit measures the transmittance of the dispersion Lq. The transmitted light measuring unit 90 has the same configuration as the particle measuring device 10a shown in Figure 10, and for example, a photomultiplier tube or photodiode is used. The complex refractive index can be determined using the measuring device 60a. Furthermore, the transmittance of the dispersion Lq is not limited to being measured with the particle measuring device 60a; the transmittance of the dispersion Lq measured in advance may also be used. For this reason, the particle measuring device 60 shown in Figure 9 can also determine the complex refractive index in the same way as the particle measuring device 60a.

[0107] The present invention is basically configured as described above. Although the particle measuring device and particle measuring method of the present invention have been described in detail above, the present invention is not limited to the embodiments described above, and various improvements or modifications may be made without departing from the spirit of the present invention. [Examples]

[0108] The features of the present invention will be further described in detail below with reference to examples. The materials, reagents, amounts and proportions of substances, and procedures shown in the following examples can be modified as appropriate without departing from the spirit of the present invention. Therefore, the scope of the present invention is not limited to the following examples. In this example, dynamic light scattering measurements of a dispersion containing particles were performed using the scattering angle as the measurement parameter. Sample 1 and Sample 2 were used as the dispersions described below. Sample 1 is an aqueous solution using pure water as the solvent and polystyrene particles as the particles. The primary particle size of the polystyrene particles is 990 nm. Note that the primary particle size of the polystyrene particles is the catalog value. Sample 2 is an aqueous solution using pure water as the solvent and titanium dioxide particles as the particles. The primary particle size of the titanium dioxide particles is 30-50 nm. Note that the primary particle size of the titanium dioxide particles is the catalog value. The particle concentration in Sample 1 is 4 × 10-4 The concentration was in mass percent. The particle concentration in sample 2 was 4 × 10⁻⁶. -3 It was in mass percent.

[0109] Using a laser beam with a wavelength of 633 nm, the time-averaged intensity of scattered light was measured under scattering angles from 30° to 160° in 5° increments, while time-dependent data were measured under scattering angles of 50°, 90°, and 140°. By measuring the scattered light intensity at each scattering angle, the autocorrelation function was determined, and the refractive index and particle size distribution of the particles were determined by fitting a theoretical formula to the autocorrelation function. Here, Figure 14 is a graph showing the particle size distribution of polystyrene particles, Figure 15 is a graph showing the relationship between the scattering intensity and scattering angle of polystyrene particles, and Figure 16 is a graph showing the second-order autocorrelation function of polystyrene particles. For Sample 1, the particle size distribution shown in Figure 14 was obtained. A refractive index of 1.56 was also obtained. The fitting was as described above. Reflecting the equation for the relative complex refractive index m described above, the values ​​of the particle number and relative complex refractive index m were updated in equations (1) and (2) above, and a fitting was performed between the measured and calculated values. The refractive index was fitted through the equation for the relative complex refractive index m described above. In this way, the final particle number and relative complex refractive index m were obtained. The particle size distribution was obtained using the final particle number.

[0110] The fitting results for Sample 1 were examined. As shown in Figure 15, the scattering intensity matched between Profile 50, which represents the measured value, and Profile 51, which was obtained through fitting. Profile 51 is the calculated value using Equation (2) described above. Furthermore, as shown in Figure 16, the second-order autocorrelation function was consistent between profile 52, which represents the measured values, and profile 53, which is obtained through fitting. The second-order autocorrelation function is the g mentioned above. (2) (τ) = 1 + β·|g (1) (τ)| 2 It was calculated using the method described above. Thus, in Sample 1, the solution converged correctly through fitting. From the obtained particle size distribution, it was also found that the particles were monodisperse in water at the primary particle size, and the conditions were such that the refractive index could be measured correctly.

[0111] Here, Figure 17 is a graph showing the particle size distribution of titanium oxide particles, Figure 18 is a graph showing the relationship between the scattering intensity and scattering angle of titanium oxide particles, and Figure 19 is a graph showing the second-order autocorrelation function of titanium oxide particles. For sample 2, the particle size distribution shown in Figure 17 was obtained. A refractive index of 2.28 was also obtained. We examined the fitting results for Sample 2. As shown in Figure 18, the scattering intensity matched between Profile 54, which represents the measured value, and Profile 55, which was obtained through fitting. Furthermore, as shown in Figure 19, the second-order autocorrelation function was consistent between profile 56, which represents the measured values, and profile 57, which is obtained through fitting. The second-order autocorrelation function is the g mentioned above. (2) (τ) = 1 + β·|g (1) (τ)| 2 It was calculated using the method described above. Thus, in Sample 2, the solution converged correctly through fitting. Furthermore, since the obtained particle size distribution was large at 300 nm, it was determined that the particles were aggregated, and the obtained refractive index was the refractive index of the nanoparticle aggregate.

[0112] The fitting process is as described above. Reflecting the equations representing the relative complex refractive index m described above, the values ​​of the particle number and relative complex refractive index m were updated in equations (1) and (2) above, and a fitting was performed between the measured and calculated values. The refractive index was fitted through the equations representing the relative complex refractive index m described above. In this way, the final particle number and relative complex refractive index m were obtained. The particle size distribution was then obtained using the final particle number. Generally, the refractive index of rutile titanium dioxide used in Sample 2 is 2.7. Since the aggregate is composed of water with a refractive index of 1.3 and titanium dioxide by volume, assuming that the refractive index changes linearly with respect to volume density, it can be estimated that in a closely packed structure, the refractive index is 2.4 at a titanium dioxide packing density of 74%, and approximately 2.28 at a packing density of 70%. In this way, the density of the aggregate can be estimated from the refractive index. The effective media approximation (EMA) may also be used to calculate the refractive index. [Examples]

[0113] In this example, dynamic light scattering measurements of a dispersion containing particles were performed using the scattering angle as a measurement parameter. Sample 3, described below, was used as the dispersion. Sample 3 used a single dispersion of Pigment Red 254 dispersed in a dispersion medium. An organic solvent with a refractive index of 1.4 was used as the dispersion medium.

[0114] The wavelength used to measure scattering intensity was set to 488 nm. The wavelength used to measure transmittance was also set to 488 nm, and the optical path length used for transmittance measurement was set to 10 mm. Using a 488 nm wavelength laser, the time-averaged intensity of scattered light was measured under scattering angles of 30° to 160° (in 10° increments), and time-dependent data was measured under scattering angles of 50°, 90°, and 150°. The autocorrelation function was determined by measuring the scattered light intensity at each scattering angle. Furthermore, using a laser beam with a wavelength of 488 nm as the incident light, the light intensity of the transmitted light was measured, and the transmittance was determined. The light intensity of the incident light was known. The complex refractive index and particle size distribution of the particles were determined by fitting theoretical formulas to the autocorrelation function, scattering intensity, and transmittance.

[0115] Here, Figure 20 is a graph showing the particle size distribution of sample 3. Figure 21 is a graph showing the relationship between the scattering intensity and scattering angle of sample 3. Figure 22 is a graph showing the second-order autocorrelation function of sample 3 at a scattering angle of 50°, Figure 23 is a graph showing the second-order autocorrelation function of sample 3 at a scattering angle of 90°, and Figure 24 is a graph showing the second-order autocorrelation function of sample 3 at a scattering angle of 150°. Figure 25 is a graph showing the transmittance of sample 3. The particle size distribution shown in Figure 20 was obtained for sample 3. The complex refractive index of sample 3 was 1.61 + 0.19i. The fitting process is as described above. Reflecting the above-mentioned equation for the relative complex refractive index m, the values ​​of the particle number and relative complex refractive index m were updated in equations (1), (2), and (4) above, and a fitting was performed between the measured and calculated values. The refractive index was fitted through the above-mentioned equation for the relative complex refractive index m. In this way, the final particle number and relative complex refractive index m were obtained. The particle size distribution shown in Figure 20 was obtained using the final particle number. The complex refractive index of the particles was obtained from the relative complex refractive index m. The complex refractive index includes not only the real part but also the imaginary part.

[0116] We examined the fitting results for Sample 3. As shown in Figure 21, the scattering intensity matched between Profile 100, which represents the measured value, and Profile 101, which was obtained through fitting. Profile 101 is the calculated value using Equation (2) described above. Furthermore, as shown in Figure 22, the second-order autocorrelation function at a scattering angle of 50° showed agreement between profile 102, which represents the measured value, and profile 103, which was obtained through fitting. As shown in Figure 23, the second-order autocorrelation function at a scattering angle of 90° showed agreement between the measured profile 104 and the fitted profile 105. As shown in Figure 24, the second-order autocorrelation function at a scattering angle of 150° showed agreement between the measured profile 106 and the fitted profile 107. The second-order autocorrelation function is the g mentioned above. (2) (τ) = 1 + β·|g(1) (τ)| 2 It was calculated using the method described above. As shown in Figure 25, the transmittance values ​​of 108 (measured) and 109 (calculated using fitting) were in agreement. The measured value of 108 is calculated using equation (3). Thus, in Sample 3, the solution converged correctly through fitting. From the obtained particle size distribution, it was also found that the particles were monodisperse in the dispersion medium with a primary particle size, and the conditions were such that the complex refractive index could be measured correctly. [Explanation of Symbols]

[0117] 10 Particle measuring device 12 Incidence setting section 13 Parameter setting section 14 Scattered light measurement section 16 sample cells 18 Arithmetic section 20 1st light source section 21a First shutter 21b Second shutter 22 Second light source section 24 Half Mirror 26, 32 Focusing lenses 28, 30 Polarizing elements 34 Light detection unit 36 Rotating part 37, 38, 39 Second-order autocorrelation function Profiles 40, 41, 42, 44, 45, 46, 47, 48 Profiles 50, 51, 52, 53, 54, 55, 56, 57 60 particle measuring device 62 Light source section 64, 70 Beam Splitter 64a, 70a Transmissive reflective surface 64c, 70b, 70c side 65, 67, 69, 76, 78 lenses 66, 75 shutters 68, 77 pinholes 71 Slits 71a opening 72, 79 Miller 73 Diffraction Grating 74 Photodetectors 80 Spectroscopic detection unit 90 Transmitted light measurement section Profiles 100, 101, 102, 103, 104, 105 106, 107 Profiles 108 Measured values 109 Fitted values C1 optical axis C 11 First axis C 12 Second axis L1 straight line Lq dispersion Ls incident light θ scattering angle

Claims

1. A particle measuring device for a dispersion containing a single type of particle, A light source unit that irradiates the dispersion with measurement light, A parameter setting unit that sets at least one of the scattering angle and measurement wavelength as a measurement parameter, A scattering light measurement unit that changes the values ​​of the measurement parameters set by the parameter setting unit multiple times, measures the scattering intensity of the scattered light emitted from the dispersion by the measurement light multiple times, and obtains multiple scattering intensity data, A particle measuring device comprising: a calculation unit that calculates time variation characteristic data of scattering intensity and parameter-dependent data of scattering intensity from the plurality of scattering intensity data obtained by the scattered light measuring unit, and a calculation unit that determines the refractive index and particle size distribution of a single type of particle by fitting the calculated time variation characteristic data of scattering intensity and the parameter-dependent data of scattering intensity using a theoretical formula that defines the relationship between refractive index, particle size, and scattering intensity or a simulation based on the theory of electromagnetic wave behavior.

2. A particle measuring device for a dispersion containing a single type of particle, A light source unit that irradiates the dispersion with measurement light, A parameter setting unit that sets at least one of the scattering angle and measurement wavelength as a measurement parameter, A scattering light measurement unit that changes the values ​​of the measurement parameters set by the parameter setting unit multiple times, measures the scattering intensity of the scattered light emitted from the dispersion by the measurement light multiple times, and obtains multiple scattering intensity data, A particle measuring device comprising: a calculation unit that calculates time variation characteristic data of scattering intensity and parameter-dependent data of scattering intensity from the plurality of scattering intensity data obtained by the scattered light measuring unit, and fits the calculated time variation characteristic data of scattering intensity, the parameter-dependent data of scattering intensity, and the transmittance data of the dispersion liquid using a simulation based on a theoretical formula defining the relationship between complex refractive index, particle size, and scattering intensity or a theory of electromagnetic wave behavior, and a simulation based on a theoretical formula defining the relationship between complex refractive index, particle size, and transmittance or a theory of electromagnetic wave behavior to determine the complex refractive index and particle size distribution of a single type of particle.

3. The particle measuring device according to claim 2, further comprising a transmittance measuring unit for measuring the transmittance of the dispersion.

4. The particle measuring device according to any one of claims 1 to 3, wherein the measurement parameter is the scattering angle, and the scattered light measuring unit changes the value of the scattering angle by two or more angles to measure the scattering intensity of the scattered light of the dispersion at multiple scattering angles and obtains multiple scattering intensity data.

5. The particle measuring device according to any one of claims 1 to 3, wherein the measurement parameter is the measurement wavelength, and the scattered light measuring unit uses two or more measurement wavelengths to measure the scattering intensity of the scattered light of the dispersion for each of the multiple measurement wavelengths to obtain a plurality of scattering intensity data.

6. The particle measuring device according to any one of claims 1 to 3, wherein the scattered light measuring unit measures the light intensity of the polarization component of the scattered light of the dispersion obtained by irradiating the dispersion with the measuring light of a specific polarization as the scattering intensity.

7. The particle measuring device according to any one of claims 1 to 3, wherein the scattered light measuring unit measures at least one of the following: parameter-dependent data of scattering intensity obtained by sequentially irradiating the dispersion with the measurement light in multiple polarization states, and parameter-dependent data of scattering intensity obtained by extracting multiple polarization components of scattered light emitted from the dispersion.

8. The particle measuring apparatus according to any one of claims 1 to 3, wherein the time variation characteristic data of the scattering intensity of the calculated measurement parameter is calculated based on the Stokes-Einstein theoretical formula, and the parameter-dependent data of the scattering intensity of the measurement parameter is calculated based on at least one of the Mie scattering theoretical formula, the discrete dipole approximation method, and the finite difference time-domain method.

9. The particle measuring device according to claim 1, wherein the calculation unit compares the refractive index of the single type of particle with the refractive index of a known material at 100% concentration, and calculates the volume concentration of the constituent material of the obtained single type of particle using the dependence of the refractive index on the particle volume concentration.

10. The particle measuring device according to claim 2, wherein the calculation unit determines the complex refractive index of a single type of particle and the particle size distribution of the number concentration by fitting the time variation characteristic data of the scattering intensity, the parameter-dependent data of the scattering intensity, the transmittance data, and the volume concentration data of the dispersion.

11. A method for measuring particles in a dispersion containing a single type of particle, At least one of the scattering angle and measurement wavelength is set as a measurement parameter. A measurement step of changing the values ​​of the set measurement parameters multiple times and measuring the scattering intensity of the scattered light emitted from the dispersion by the measurement light multiple times, A calculation step is performed to calculate time variation characteristic data of scattering intensity and parameter-dependent data of scattering intensity from a plurality of scattering intensity data obtained by the measurement step described above. A step of fitting the time variation characteristic data of the scattering intensity and the parameter-dependent data of the scattering intensity obtained in the calculation step above using a theoretical formula that defines the relationship between refractive index, particle size, and scattering intensity, or a simulation based on the theory of electromagnetic wave behavior, A method for measuring particles, comprising the steps of determining the refractive index and particle size distribution of a single type of particle in the dispersion.

12. A method for measuring particles in a dispersion containing a single type of particle, At least one of the scattering angle and measurement wavelength is set as a measurement parameter. A measurement step of changing the values ​​of the set measurement parameters multiple times and measuring the scattering intensity of the scattered light emitted from the dispersion by the measurement light multiple times, A calculation step is performed to calculate time variation characteristic data of scattering intensity and parameter-dependent data of scattering intensity from a plurality of scattering intensity data obtained by the measurement step described above. A method for measuring particles, comprising the step of determining the complex refractive index and particle size distribution of a single type of particle by fitting the transmittance data of the dispersion, the time variation characteristic data of the scattering intensity and the parameter-dependent data of the scattering intensity obtained in the calculation step, using a simulation based on a theoretical formula defining the relationship between the complex refractive index, particle size, and scattering intensity or a theory of electromagnetic wave behavior, and a simulation based on a theoretical formula defining the relationship between the complex refractive index, particle size, and transmittance or a theory of electromagnetic wave behavior.

13. The particle measurement method according to claim 12, further comprising the step of measuring the transmittance of the dispersion and obtaining the transmittance data.

14. The particle measurement method according to any one of claims 11 to 13, wherein the measurement parameter is the scattering angle, and the measurement step is to change the value of the scattering angle by two or more angles and measure the scattering intensity of the scattered light of the dispersion for each of the multiple scattering angles.

15. The particle measurement method according to any one of claims 11 to 13, wherein the measurement parameter is the measurement wavelength, and the measurement step is to measure the scattering intensity of the scattered light of the dispersion for each of the multiple measurement wavelengths using two or more of the measurement wavelengths.

16. The particle measurement method according to any one of claims 11 to 13, wherein the measurement step involves irradiating the dispersion with measurement light of a specific polarization and measuring the light intensity of the polarization component of the scattered light of the dispersion as the scattering intensity.

17. The particle measurement method according to any one of claims 11 to 13, wherein the measurement step measures at least one of the following: parameter-dependent data of scattering intensity obtained by sequentially irradiating the dispersion with the measurement light in multiple polarization states, and parameter-dependent data of scattering intensity obtained by extracting multiple polarization components of scattered light emitted from the dispersion.

18. The method for measuring particles according to any one of claims 11 to 13, wherein the time variation characteristic data of the scattering intensity of the calculated measurement parameter is calculated based on the Stokes-Einstein theoretical formula, and the parameter-dependent data of the scattering intensity of the measurement parameter is calculated based on at least one of the Mie scattering theoretical formula, the discrete dipole approximation method, and the finite difference time-domain method.

19. The particle measurement method according to claim 11, further comprising the step of comparing the refractive index of the obtained single type of particle with the refractive index of a known material at 100% concentration, and calculating the volume concentration of the constituent material of the obtained single type of particle using the dependence of the refractive index on the particle volume concentration.

20. The particle measurement method according to claim 12, wherein the complex refractive index of a single type of particle and the particle size distribution of the number concentration are determined by fitting the time variation characteristic data of the scattering intensity, the parameter-dependent data of the scattering intensity, the transmittance data, and the volume concentration data of the dispersion.

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