CN117501094A - Particle measurement device and particle measurement method - Google Patents
Particle measurement device and particle measurement method Download PDFInfo
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- CN117501094A CN117501094A CN202280042838.XA CN202280042838A CN117501094A CN 117501094 A CN117501094 A CN 117501094A CN 202280042838 A CN202280042838 A CN 202280042838A CN 117501094 A CN117501094 A CN 117501094A
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Abstract
Provided are a particle measurement device and a particle measurement method capable of measuring the refractive index, complex refractive index and particle size distribution of a single particle contained in a dispersion liquid. The scattering particle measurement device comprises: a light source unit that irradiates a dispersion liquid containing a single type of particles with measurement light; a parameter setting unit that sets at least one of a scattering angle and a measurement wavelength as a measurement parameter; a scattered light measurement unit that changes the values of a plurality of set measurement parameters, and measures the scattered intensity of scattered light emitted from the dispersion liquid by the measurement light a plurality of times, thereby obtaining a plurality of pieces of scattered intensity data; and a calculation unit for calculating time-varying characteristic data of the scattering intensity and parameter-dependent data of the scattering intensity from the plurality of scattering intensity data, and obtaining refractive index and particle size distribution of the single particle by fitting the calculated time-varying characteristic data of the scattering intensity and parameter-dependent data of the scattering intensity by using a theoretical formula based on a relation between a predetermined refractive index, particle size and scattering intensity or a simulation of electromagnetic wave behavior theory.
Description
Technical Field
The present invention relates to a particle measurement device and a particle measurement method for measuring refractive index of a single particle contained in a dispersion liquid.
Background
There is a dynamic light scattering measurement method that detects a temporal change in the intensity of scattered light scattered from a scatterer in a medium such as a colloidal solution or a particle dispersion by applying light to the medium using an autocorrelation function or a power spectrum, thereby investigating the dynamic characteristics of the scatterer. Dynamic light scattering measurement is widely used for various measurements such as particle size measurement and structural analysis of gel.
For example, patent document 1 describes a particle diameter measuring apparatus including: a laser device for irradiating a group of particles to be measured with a laser beam; a measurement system for measuring, as a scattered light intensity distribution, an intensity of each scattering angle of scattered light emitted from the laser device and scattered by the particle group to be measured; a relative particle size distribution calculating unit for calculating a relative particle size distribution from the measurement value of the scattered light intensity distribution obtained by the measuring system; a conversion table storing conversion coefficients of the ratio of the measured value of the scattered light intensity distribution obtained by irradiating a laser beam to a reference particle group having a particle diameter and a particle diameter density known in advance, to the theoretical value, for each scattering angle; a conversion unit that converts the measured value of the scattered light intensity distribution obtained by irradiating the laser beam to the particle group to be measured according to the conversion table, thereby obtaining an incident scattered light intensity distribution in the incident portion of the measurement system; and an absolute particle size distribution calculating unit that calculates an absolute particle size distribution from the incident scattering intensity distribution obtained by the converting unit and the relative particle size distribution of the measured particle group obtained by the relative particle size distribution calculating unit.
Prior art literature
Patent literature
Patent document 1: japanese patent publication No. 2-63181
Disclosure of Invention
Technical problem to be solved by the invention
As described above, patent document 1 describes the following: the absolute particle size distribution is calculated by using the scattered light intensity distribution for each scattering angle of the scattered light scattered by the particle group to be measured. However, patent document 1 can measure the particle size distribution, but cannot measure the refractive index of particles.
Although there is a need to obtain information on the refractive index of the particles to be measured, it is not possible to obtain information on the refractive index at present.
The purpose of the present invention is to provide a particle measurement device and a particle measurement method that are capable of measuring the refractive index, complex refractive index, and particle size distribution of a single type of particles contained in a dispersion liquid.
Means for solving the technical problems
In order to achieve the above object, the invention [1] provides a particle measurement device for measuring particles including a dispersion of particles of a single type, comprising: a light source unit for irradiating the dispersion with measurement light; a parameter setting unit that sets at least one of a scattering angle and a measurement wavelength as a measurement parameter; a scattered light measurement unit that changes the values of the plurality of measurement parameters set by the parameter setting unit, and measures the scattered intensity of scattered light emitted from the dispersion liquid by the measurement light a plurality of times, thereby obtaining a plurality of pieces of scattered intensity data; and a calculation unit for calculating time-varying characteristic data of the scattering intensity and parameter-dependent data of the scattering intensity from the plurality of scattering intensity data obtained by the scattered light measurement unit, and obtaining refractive index and particle diameter distribution of the single particle by fitting the calculated time-varying characteristic data of the scattering intensity and parameter-dependent data of the scattering intensity by using a theoretical formula based on a relation between a predetermined refractive index, particle diameter and scattering intensity or simulation of electromagnetic wave behavior theory.
The invention [2] provides a particle measurement device for measuring particles comprising a dispersion of particles of a single type, comprising: a light source unit for irradiating the dispersion with measurement light; a parameter setting unit that sets at least one of a scattering angle and a measurement wavelength as a measurement parameter; a scattered light measurement unit that changes the values of the measurement parameters set by the parameter setting unit, and measures the scattered intensity of scattered light emitted from the dispersion liquid by the measurement light a plurality of times to obtain a plurality of pieces of scattered intensity data; and a calculation unit for calculating time-varying characteristic data of the scattering intensity and parameter-dependent data of the scattering intensity from the plurality of scattering intensity data obtained by the scattered light measurement unit, and obtaining complex refractive index and particle size distribution of the single particle by fitting the calculated time-varying characteristic data of the scattering intensity and parameter-dependent data of the scattering intensity to transmittance data of the dispersion using a theoretical formula based on a relationship between a predetermined complex refractive index, particle size and scattering intensity, or a simulation of electromagnetic wave behavior theory, and a theoretical formula based on a relationship between a predetermined complex refractive index, particle size and transmittance, or a simulation of electromagnetic wave behavior theory.
The invention [3] is the particle measurement device according to the invention [2], which comprises a transmittance measurement unit for measuring the transmittance of the dispersion.
The invention [4] is the particle measurement device according to any one of the inventions [1] to [3], wherein the measurement parameter is a scattering angle, and the scattered light measurement unit changes a value of the scattering angle by two or more angles and measures a scattering intensity of scattered light of the dispersion liquid for each of the plurality of scattering angles to obtain a plurality of scattering intensity data.
The invention [5] is the particle measurement device according to any one of the inventions [1] to [3], wherein the measurement parameter is a measurement wavelength, and the scattered light measurement unit obtains a plurality of pieces of scattered intensity data by measuring the scattered intensity of scattered light of the dispersion liquid for each of a plurality of measurement wavelengths using two or more measurement wavelengths.
The invention [6] is the particle measurement device according to any one of the inventions [1] to [5], wherein the scattered light measurement unit measures, as the scattered intensity, the light intensity of the polarized component of scattered light of the dispersion obtained by irradiating the dispersion with measurement light of a specific polarized light.
The invention [7] is the particle measurement device according to any one of the inventions [1] to [6], wherein the scattered light measurement unit measures at least one of parameter-dependent data of scattered intensity obtained by sequentially irradiating a dispersion with a plurality of polarized measurement lights and parameter-dependent data of scattered intensity obtained by taking out polarization components of a plurality of scattered lights emitted from the dispersion.
The invention [8] is the particle measurement device according to any one of the inventions [1] to [7], wherein the time-varying characteristic data of the scattering intensity of the measurement parameter calculated is calculated from a stokes-einstein theoretical formula, and the parameter-dependent data of the scattering intensity of the measurement parameter is calculated from at least one of a mie scattering theoretical formula, a discrete dipole approximation method, and a time-domain finite difference method.
The invention [9] is the particle measurement device according to any one of the inventions [1] and [4] to [8], wherein the calculation unit compares the refractive index of the single particle type with the refractive index of the known material at 100% concentration, and calculates the volume concentration of the constituent substance of the single particle type using the dependence of the refractive index on the volume concentration of the particle.
The invention [10] is the particle measurement device according to the invention [2], wherein the calculation unit calculates a particle diameter distribution of complex refractive index and number concentration of a single particle by fitting using time-varying characteristic data of scattering intensity, parameter-dependent data of scattering intensity, transmittance data, and volume concentration data of dispersion.
The invention [11] provides a method for measuring particles, which is a method for measuring particles comprising a dispersion of particles of a single type, comprising the steps of: a measurement step of setting at least one of a scattering angle and a measurement wavelength as a measurement parameter, and changing the values of the plurality of set measurement parameters to measure the scattering intensity of scattered light emitted from the dispersion liquid by the measurement light a plurality of times; a calculation step of calculating time variation characteristic data of the scattering intensity and scattering intensity parameter dependent data from the plurality of scattering intensity data obtained in the measurement step; fitting the time variation characteristic data of the scattering intensity and the parameter dependent data of the scattering intensity obtained by the calculation step by using a theoretical formula based on a relation between a predetermined refractive index, a particle diameter, and the scattering intensity or a simulation of an electromagnetic wave behavior theory; and a step of determining the refractive index and the particle diameter distribution of the single type of particles in the dispersion.
The invention [12] provides a method for measuring particles, which is a method for measuring particles comprising a dispersion of particles of a single type, comprising the steps of: a measurement step of setting at least one of a scattering angle and a measurement wavelength as a measurement parameter, and changing the values of the plurality of set measurement parameters to measure the scattering intensity of scattered light emitted from the dispersion liquid by the measurement light a plurality of times; a calculation step of calculating time variation characteristic data of the scattering intensity and scattering intensity parameter dependent data from the plurality of scattering intensity data obtained in the measurement step; and a step of obtaining the complex refractive index and the particle size distribution of the single particle by fitting the transmittance data of the dispersion liquid to the time-varying characteristic data of the scattering intensity and the parameter-dependent data of the scattering intensity obtained in the calculation step by using a theoretical formula or simulation of the electromagnetic wave behavior theory based on the relation between the prescribed complex refractive index, the particle size and the scattering intensity and a theoretical formula or simulation of the electromagnetic wave behavior theory based on the relation between the prescribed complex refractive index, the particle size and the transmittance.
The invention [13] is the method for measuring particles according to the invention [12], comprising a step of measuring the transmittance of the dispersion liquid to obtain transmittance data.
The invention [14] is the method for measuring particles according to any one of the inventions [11] to [13], wherein the measurement parameter is a scattering angle, and in the measuring step, the scattering intensity of scattered light of the dispersion is measured for each of a plurality of scattering angles by changing the value of the scattering angle by two or more angles.
The invention [15] is the method for measuring particles according to any one of the inventions [11] to [13], wherein the measurement parameter is a measurement wavelength, and in the measuring step, the scattering intensity of scattered light of the dispersion liquid is measured for each of a plurality of measurement wavelengths using two or more measurement wavelengths.
The invention [16] is the method for measuring particles according to any one of the inventions [11] to [15], wherein in the measuring step, the light intensity of the polarized component of scattered light of the dispersion obtained by irradiating the dispersion with the measurement light of a specific polarized light is measured as the scattering intensity.
The invention [17] is the method for measuring particles according to any one of the inventions [11] to [16], wherein,
in the measurement step, at least one of parameter-dependent data of scattering intensity obtained by sequentially irradiating the dispersion with measurement light in a plurality of polarization states and parameter-dependent data of scattering intensity obtained by taking out polarization components of the plurality of scattered light emitted from the dispersion is measured.
The invention [18] is the method for measuring particles according to any one of the inventions [11] to [17], wherein the time-varying characteristic data of the scattering intensity of the measurement parameter calculated is calculated from a stokes-einstein theoretical formula, and the parameter-dependent data of the scattering intensity of the measurement parameter is calculated from at least one of a mie scattering theoretical formula, a discrete dipole approximation method, and a time-domain finite difference method.
The invention [19] is the method for measuring particles according to any one of the inventions [11] and [14] to [18], further comprising the steps of: and a step of comparing the refractive index of the obtained single-type particles with the refractive index of the known material at 100% concentration, and calculating the volume concentration of the constituent substance constituting the obtained single-type particles using the dependence of the refractive index on the volume concentration of the particles.
The invention [20] is the method for measuring particles according to the invention [12], wherein the particle size distribution of the complex refractive index and the number concentration of the single particle is obtained by fitting using the time-varying 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.
Effects of the invention
According to the present invention, it is possible to provide a particle measurement device and a particle measurement method capable of measuring the refractive index, complex refractive index, and particle size distribution of a single type of particles contained in a dispersion liquid.
Drawings
FIG. 1 is a schematic view showing example 1 of a particle measurement apparatus according to an embodiment of the present invention.
Fig. 2 is a flowchart showing example 1 of a method for measuring particles according to an embodiment of the present invention.
FIG. 3 is a graph showing an example of the relationship between the scattering intensity and the scattering angle of an aqueous dispersion of polystyrene particles.
Fig. 4 is a graph showing an example of the second-order autocorrelation function for each scattering angle.
Fig. 5 is a graph showing calculated values of scattering angle and scattering intensity for each refractive index of particles having the same particle size.
Fig. 6 is a graph showing an example of the relationship between the scattering intensity and the measurement wavelength.
Fig. 7 is a graph showing another example of the relationship between the scattering intensity and the measurement wavelength.
Fig. 8 is a graph showing the relationship between the scattering intensity and the scattering angle for each shape of particle.
Fig. 9 is a schematic diagram showing example 2 of a particle measurement apparatus according to an embodiment of the present invention.
FIG. 10 is a schematic view showing example 3 of a particle measurement apparatus according to an embodiment of the present invention.
Fig. 11 is a histogram of particles.
Fig. 12 is a flowchart showing example 2 of a method for measuring particles according to an embodiment of the present invention.
FIG. 13 is a schematic view showing example 4 of a particle measurement apparatus according to an embodiment of the present invention.
FIG. 14 is a graph showing the particle size distribution of polystyrene particles.
Fig. 15 is a graph showing a relationship between scattering intensity and scattering angle of polystyrene particles.
Fig. 16 is a graph showing a second order autocorrelation function of polystyrene particles.
Fig. 17 is a graph showing the particle size distribution of titanium oxide particles.
Fig. 18 is a graph showing a relationship between scattering intensity and scattering angle of titanium oxide particles.
Fig. 19 is a graph showing a second-order autocorrelation function of titanium oxide particles.
FIG. 20 is a graph showing the particle size distribution of sample 3.
Fig. 21 is a graph showing the relationship between the scattering intensity and the scattering angle of sample 3.
Fig. 22 is a graph showing the second order autocorrelation function of sample 3 at a scattering angle of 50 °.
Fig. 23 is a graph showing the second order autocorrelation function of sample 3 at a scattering angle of 90 °.
Fig. 24 is a graph showing the second order autocorrelation function of sample 3 at a scattering angle of 150 °.
Fig. 25 is a graph showing the transmittance of sample 3.
Detailed Description
The apparatus and method for measuring particles according to the present invention will be described in detail below with reference to preferred embodiments shown in the drawings.
The drawings described below are illustrative drawings for explaining the present invention, and the present invention is not limited to the drawings described below.
In the following, the term "to" representing the numerical range includes numerical values described on both sides. For example, ε is a numerical value ε A Number epsilon B Meaning that the range of epsilon comprises the value epsilon A Sum value epsilon B If expressed in mathematical notation, is epsilon A ≤ε≤ε B 。
Unless otherwise specified, angles such as "angle represented by a specific numerical value" and "vertical" include the range of errors generally allowed in the corresponding technical field.
(example 1 of particle measurement apparatus)
FIG. 1 is a schematic view showing example 1 of a particle measurement apparatus according to an embodiment of the present invention.
The particle measurement device 10 shown in fig. 1 includes: the sample cell 16 containing the dispersion liquid Lq containing the single type of particles is irradiated with a laser beam as the incidence setting unit 12 of the measurement light, the scattered light measuring unit 14 for measuring the scattering intensity of the scattered light generated by scattering the laser beam in the dispersion liquid Lq, and the calculation unit 18 for obtaining the refractive index and the particle diameter distribution of the single type of particles contained in the dispersion liquid. The complex refractive index has a real part and an imaginary part, the real part of the complex refractive index being called the so-called refractive index. The imaginary part of the complex refractive index is called the extinction coefficient representing the absorption. When the transmittance of the particles is high, the imaginary part of the complex refractive index becomes a value close to zero.
The incidence setting unit 12 includes: the liquid crystal display device includes a 1 st light source unit 20 that emits a laser beam as measurement light to the dispersion liquid Lq, a 2 nd light source unit 22 that emits a laser beam as measurement light to the dispersion liquid Lq, a half mirror 24, a condensing lens 26 that condenses the laser beam transmitted or reflected by the half mirror 24 in the sample cell 16, and a polarizing element 28 that transmits only a certain polarized component in the laser beam. A 1 st shutter 21a is provided between the 1 st light source unit 20 and the half mirror 24. A 2 nd shutter 21b is provided between the 2 nd light source portion 22 and the half mirror 24. The 1 st shutter 21a allows the laser beam emitted from the 1 st light source unit 20 to enter the half mirror 24 or to be blocked for preventing the incidence. The 2 nd shutter 21b allows the laser beam emitted from the 2 nd light source 22 to enter the half mirror 24 or to be blocked for preventing the incidence.
The 1 st shutter 21a and the 2 nd shutter 21b are not particularly limited as long as they can make the emitted laser beam incident on the half mirror 24 or block the same, and known on/off shutters used for controlling the emission of the laser beam can be used.
In addition to the 1 st shutter 21a and the 2 nd shutter 21b, for example, the emission of the 1 st light source unit 20 and the emission of the 2 nd light source unit 22 may be controlled to control the emission of the laser beam to the half mirror 24.
The half mirror 24 transmits the laser beam emitted from the 1 st light source portion 20 and reflects the laser beam emitted from the 2 nd light source portion 22 along the same optical path as the laser beam emitted from the 1 st light source portion 20, for example, at 90 ° with respect to the incident direction. Transmitted by half-reflectionThe laser beam of the mirror 24 and the laser beam reflected by the half mirror 24 pass through the same optical axis C 1 . On the optical axis C 1 A condenser lens 26 and a polarizing element 28 are disposed thereon. On the optical axis C 1 A sample cell 16 is disposed thereon.
In addition, on the optical axis C of the laser beam 1 A shutter (not shown) for temporarily cutting off the optical path of the laser beam and an ND (Neutral Density) filter (not shown) for attenuating the laser beam may be provided.
The ND filter is used to adjust the light amount of the laser beam, and a known filter can be used as appropriate.
The polarizing element 28 may be appropriately used in accordance with polarized light irradiated to the sample cell 16, such as circularly polarized light, linearly polarized light, or elliptically polarized light. In addition, polarizing element 28 is not necessarily required when it is not necessary to irradiate polarized light to sample cell 16.
The 1 st light source unit 20 irradiates the dispersion Lq with a laser beam as measurement light for the dispersion Lq, and is an Ar laser that emits a laser beam having a wavelength of 488nm, for example. The wavelength of the laser beam is not particularly limited.
The 2 nd light source unit 22 irradiates the dispersion Lq with a laser beam as measurement light for the dispersion Lq, for example, a he—ne laser that emits a laser beam having a wavelength of 633 nm. The wavelength of the laser beam is not particularly limited.
The wavelength of the laser beam of the 1 st light source section 20 is different from that of the laser beam of the 2 nd light source section 22. In the particle measurement apparatus 10, the appropriate wavelength differs depending on the target particle to be measured. Therefore, it is desirable to select a combination of wavelengths in which the refractive index differences of the plurality of particles are greatly different from one wavelength to another.
The incidence setting unit 12 sets at least one of the scattering angle and the measurement wavelength as a measurement parameter. As the measurement parameter, there are a scattering angle or a combination of a measurement wavelength and a scattering angle. In the measurement parameter, the scattering angle is set to two or more angles, or the measurement wavelength is set to two or more wavelengths.
Here, the two angles refer to the number of scattering angles. The two angles are, for example, scattering angles 45 ° and 90 °.
The two wavelengths are the number of measurement wavelengths. The two wavelengths are for example wavelength 633nm and wavelength 488nm.
The scattering angle can be changed by rotating the scattered light measuring section 14 around the sample cell 16 by a rotation section 36 described later, for example, and can be set to two or more angles. The parameter setting unit 13 is constituted by an incidence setting unit 12 and a rotation unit 36 described later. As described above, at least one of the scattering angle and the measurement wavelength is set as the measurement parameter by the parameter setting unit 13.
The measurement wavelength can be changed by switching between the 1 st light source unit 20 and the 2 nd light source unit 22, and the measurement wavelength can be two or more wavelengths. For example, laser beams having different wavelengths are emitted from the 1 st light source unit 20 and the 2 nd light source unit 22 as measurement light.
Therefore, the configuration having the light source units corresponding to the number of measurement wavelengths is not limited to the 1 st light source unit 20 and the 2 nd light source unit 22. When the measurement wavelength is not changed, one of the 1 st light source unit 20 and the 2 nd light source unit 22 may be present. Also, a light source may be added to increase the number of measured wavelengths.
The sample cell 16 is a rectangular parallelepiped or cylindrical container made of optical glass or optical plastic, for example. The sample cell 16 accommodates a dispersion Lq containing particles of a single type as a measurement target. The laser beam is irradiated to the dispersion Lq as measuring light to the dispersion Lq.
The sample cell 16 may be disposed inside a liquid immersion bath (not shown). The liquid immersion bath is used to remove the refractive index difference or homogenize the temperature.
As described above, the scattered light measuring unit 14 measures the scattered light intensity of the scattered light generated by scattering the laser beam in the dispersion Lq.
The scattered light measuring unit 14 changes the values of the plurality of measurement parameters set by the parameter setting unit 13, and measures the scattered intensity of scattered light emitted from the dispersion Lq by the measurement light a plurality of times, thereby obtaining a plurality of pieces of scattered intensity data. Examples of the multiple measurement of the scattering intensity of scattered light include measurement at each of a plurality of scattering angles and measurement at each of a plurality of measurement wavelengths.
The scattered light measuring section 14 includes a polarizing element 30 that transmits only a certain polarization component of the scattered light from the sample cell 16, a condenser lens 32 that forms an image of the scattered light on a light detecting section 34, and a light detecting section 34 that detects the scattered light.
In order to appropriately set the scattering volume of the sample, a 1 st pinhole (not shown) and a 2 nd pinhole (not shown) may be provided.
The polarizing element 30 may be appropriately a polarizing element corresponding to polarized light to be detected, such as circularly polarized light, linearly polarized light, or elliptically polarized light. The polarizing element 30 may be provided with a polarizing element for detecting circularly polarized light and a polarizing element for detecting linearly polarized light, and the light intensity of each polarized component of scattered light may be detected by the light detecting unit 34 by switching the polarized light to be detected.
In addition, when it is not necessary to measure the light intensity of the polarized component of scattered light, the polarizing element 30 is not necessarily required.
The light detection unit 34 is not particularly limited as long as it can detect the intensity of scattered light, and for example, a photomultiplier tube, a photodiode, an avalanche photodiode, a time correlator, or the like can be used.
The light source further includes a rotating unit 36 for rotating 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 portion 36. The angle of the scattering angle θ is the scattering angle. In fig. 1, the angle of the scattering angle is 90 °. I.e. the scattering angle is 90 deg.. For example, a goniometer may be used for the rotating portion 36. For example, the scattered light measuring section 14 is placed on a goniometer as the rotating section 36, and the scattering angle θ is adjusted by the goniometer.
As described above, the particle measurement apparatus 10 can perform dynamic light scattering measurement using two or more measurement wavelengths by including the 1 st light source unit 20 and the 2 nd light source unit 22 which emit different laser beams, and can obtain a plurality of scattering intensity data for particles in the dispersion Lq.
Further, as described above, the particle measurement apparatus 10 has the rotation unit 36 for rotating the scattered light measurement unit 14, and can change the angle of the scattering angle θ, that is, the value of the scattering angle, by two or more angles to perform dynamic light scattering measurement, whereby a plurality of pieces of scattered intensity data can be obtained for the particles in the dispersion Lq.
The calculation unit 18 obtains the refractive index and the particle size distribution of particles in the dispersion Lq containing particles of a single type based on the intensity of the scattered light detected by the light detection unit 34. The calculation unit 18 stores a theoretical formula for defining a relationship between refractive index, particle diameter, and scattering intensity, which will be described later, and performs fitting, which will be described later. The calculation unit 18 can calculate the particle count in addition to the refractive index and the particle size distribution of the particles.
The calculation unit 18 calculates time-varying characteristic data of a plurality of scattering intensities of the measurement parameters and parameter-dependent data of a plurality of scattering intensities of the measurement parameters from the plurality of scattering intensity data obtained by the scattered light measurement unit 14, and fits the calculated time-varying characteristic data of a plurality of scattering intensities of the measurement parameters and the calculated parameter-dependent data of a plurality of scattering intensities of the measurement parameters by using a theoretical formula based on a relation between a predetermined refractive index, particle diameter, and scattering intensity or simulation of electromagnetic wave behavior theory, thereby obtaining refractive index and particle diameter distribution of single particles. The fitting will be described later.
In addition to the theoretical formula that defines the relationship between refractive index, particle diameter, and scattering intensity, time-varying characteristic data of scattering intensity of a measurement parameter calculated by simulation based on electromagnetic wave behavior theory and parameter-dependent data of scattering intensity of the calculated measurement parameter may be used.
In the computing unit 18, the time-varying characteristic data of the scattering intensity of the calculated measurement parameter is calculated from a stokes-einstein theoretical formula. And, for example, parameter-dependent data of the scattering intensity is calculated from at least one of a Mie (Mie) scattering theory formula, a discrete dipole approximation method (DDA method), and a time-finite difference method (FDTD method). In addition, the discrete dipole approximation method (DDA method) and the time-finite difference method (FDTD method) correspond to simulations based on the theory of electromagnetic wave behavior. The method equivalent to the simulation based on the electromagnetic wave behavior theory can be appropriately utilized, and is not particularly limited to the discrete dipole approximation method (DDA method) and the time-finite difference method (FDTD method) described above.
The theoretical formula is not particularly limited to the above formula, and various theoretical formulas such as scattering theory can be appropriately used.
The arithmetic unit 18 obtains the particle size distribution of particles as described above by executing a program (computer software) stored in a ROM (Read Only Memory) or the like in the arithmetic unit 18. The computing unit 18 may be configured by a computer that functions each part by executing the program as described above, may be a dedicated device configured by a dedicated circuit for each part, or may be configured by a server so as to be executed on the cloud.
When measuring the scattering intensity of the dispersion, there is a scattering angle as a measurement parameter. When the measurement parameter is a scattering angle, the scattering intensity of the dispersion is measured for each of a plurality of scattering angles by changing the value of the scattering angle by two or more angles as the value of the measurement parameter. In this case, for example, the measurement wavelength is fixed to one.
When the measurement parameter is the measurement wavelength of the measurement light, the scattering intensity of the dispersion is measured for each of the plurality of measurement wavelengths using two or more measurement wavelengths. In this case, for example, the scattering angle is fixed to one. The two wavelengths are values of the measurement parameters.
As the measurement parameter, there is a case where the scattering angle and the measurement wavelength are used. In this case, the scattering intensity of the dispersion is measured for each combination of the scattering angle and the measurement wavelength by setting the value of the scattering angle to two or more angles and to two or more measurement wavelengths.
The scattering angle is not particularly limited as long as the value thereof is two or more, and may be appropriately determined from the number of scattering intensity data, the measurement time, and the like. As the value of the scattering angle, more than 0 ° and 180 ° are preferable.
The measurement wavelength is not particularly limited as long as it is two or more wavelengths. The measurement wavelength can be appropriately determined in consideration of the case where a large number of light sources are required or an optical element for dividing the wavelength is required when the measurement wavelength is increased.
The measurement wavelength is not particularly limited, and light of each wavelength such as ultraviolet light, visible light, and infrared light can be appropriately used.
In addition, as described above, the scattering intensity can be measured by a dynamic light scattering measurement method or can be measured by one measuring device in combination with the device, but it is also possible to use the measurement data of two different devices, namely, a dynamic light scattering device, a light scattering goniometer, and a combination thereof. In the case of wavelength, a beam splitter may be used. As described above, the apparatus is not limited to the measurement apparatus 10 using the particles shown in fig. 1, for example.
The particles in the dispersion are unitary. That is, assuming that the particles in the dispersion are one type, a theoretical formula defining the relationship between refractive index, particle diameter and scattering intensity is set to determine the refractive index and particle diameter distribution of the single type of particles.
(example 1 of particle measurement method)
Fig. 2 is a flowchart showing example 1 of a method for measuring particles according to an embodiment of the present invention.
In example 1 of the particle measurement method, the measurement parameter is a scattering angle, and the scattering intensity of the dispersion liquid is measured for each of a plurality of scattering angles by changing the value of the scattering angle by two or more angles.
As shown in fig. 2, the particle measurement method includes, for example, a measurement step (step S10), a step of obtaining experimental data (step S12), and an optimization step (step S14). By the optimization step (step S14), the analysis results (step S16), that is, the refractive index (real part of complex refractive index) and the particle size distribution of the single kind of particles (step S16) can be obtained. The particle size distribution refers to a distribution of the number of particles relative to the particle size, for example, expressed in%.
The measurement step (step S10) measures, for example, the scattering angle dependence of the time-averaged value of the scattering intensity.
The step of obtaining experimental data (step S12) obtains, for example, an autocorrelation function of the scattering intensity with respect to time fluctuation from the measurement value in the measurement step (step S10). And, a time average value of the scattering angle-dependent or wavelength-dependent scattering intensity of the time average value of the scattering intensity is obtained. Thus, for example, the scattering intensity for each scattering angle shown in fig. 3 can be obtained.
In the optimization step (step S14), for example, a theoretical formula of the autocorrelation function and the scattering intensity is fitted to the autocorrelation function of the temporal fluctuation of the scattering intensity and the temporal average value of the scattering intensity obtained in step S12. In step S14, after an initial value is set for the particle number of the particle size of the single particle, the final particle number is obtained by updating the evaluation value to be the smallest. In addition, the initial value is set by generating a random variable.
Hereinafter, the method for measuring particles including fitting will be described in detail.
First, for example, a laser beam having a wavelength of 633nm is irradiated from the 2 nd light source unit 22 shown in fig. 1 to the dispersion liquid Lq. The scattered light scattered by the irradiation is detected by the photodetector 34 for a predetermined time at a predetermined scattering angle. This can obtain the scattering intensity of the dispersion Lq at the scattering angle.
Then, the scattered light measuring unit 14 is rotated by the rotating unit 36 to change the scattering angle θ, thereby obtaining the scattering intensity of the dispersion liquid Lq. The scattering intensity of the dispersion Lq was measured by repeating the change of the scattering angle and the measurement of the scattering intensity of the dispersion Lq. The scattering angle is two or more, and the scattering intensity is measured every 5 ° from 30 ° to 160 °. The above steps are measurement steps, and correspond to step S10 described above.
Next, the calculating unit 18 calculates time-varying characteristic data of the scattering intensity from the time-dependence of the scattering intensity of the dispersion Lq obtained in the measuring step. The time-varying characteristic data of the scattering intensity is 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-varying characteristic data of the scattering intensity is obtained for each scattering angle. That is, there are a plurality of time varying data.
Next, the calculating unit 18 calculates parameter-dependent data of the scattering intensity from the scattering intensity of the dispersion liquid obtained in the measuring step.
The parameter-dependent data of the scattering intensity of the dispersion liquid is obtained by calculating, for example, a time average value of the scattering intensity of the dispersion liquid for each scattering angle. Thus, for example, data of the scattering intensity for each scattering angle as shown in fig. 3 is obtained.
The step of calculating the time-varying characteristic data of the scattering intensity of the dispersion and the parameter-dependent data of the scattering intensity of the dispersion as described above is a calculation step, and corresponds to step S12 described above.
Next, the calculation unit 18 uses a theoretical formula based on a relationship between a predetermined refractive index, particle diameter, and scattering intensity or a simulation of electromagnetic wave behavior theory to fit time-varying characteristic data of scattering intensity at least one scattering angle and parameter-dependent data of scattering intensity at a plurality of scattering angles. The refractive index (real part of complex refractive index) and the particle size distribution of the single type of particles were obtained by this fitting. This corresponds to steps S14 and S16 described above.
As described above, one kind of particles is contained in the dispersion.
The first order autocorrelation function is defined by g (1) (τ)＝exp(-Dq 2 τ) represents. The relationship between the diffusion coefficient and the particle size obtained from the autocorrelation function is applicable to stokes-einstein's formula for a general dynamic light scattering method.
When the particles have a particle size distribution, the first-order autocorrelation function is represented by the following formula (1). The scattering intensity is expressed by the following formula (2). The following formulas (1) and (2) are theoretical formulas, I of formulas (1) and (2) θ total Are all calculated values.
[ number 1]
[ number 2]
In formula (1), g (1) Representing a first order autocorrelation function. The first-order autocorrelation function of equation (1) is a first-order autocorrelation function for each scattering angle. The scattering intensity of the formula (2) is the scattering intensity for each scattering angle. Therefore, the formulas (1) and (2) are obtained for each scattering angle to be measured.
In the formulas (1) and (2), I θ total Indicating the total scattering intensity. d represents the particle size. The subscripts 0-M of d denote the ordinals of the bins of the histogram of the particles. N represents the number of particles. D represents the diffusion coefficient. The subscript D of the diffusion coefficient D indicates a dependence on the particle diameter D. q represents a scattering vector. τ represents the time lag of the first order autocorrelation function. θ represents the scattering angle. I represents the scattering intensity. The subscript d of the scattering intensity I indicates a dependence on the particle size d. The subscript θ of the scattering intensity I indicates dependence on the scattering angle θ. The bin of the histogram refers to a data bin of the histogram, and is represented by a bar in the histogram.
N d I d,θ /I θ total The ratio of the scattering intensity based on all single particles belonging to the section of particle diameter d relative to the total scattering intensity.
The scattering intensity of the particles with respect to the particle diameter d and the relative complex refractive index m is given by the following formula by the Mie (Mie) scattering theory. The following formula is a theoretical formula defining the relationship between refractive index, particle diameter and scattering intensity.
[ number 3]
Here, P l The subscript l represents the degree of the polynomial of Legendre (Legendre) and represents the function obtained by partial differentiation of the Legendre (Legendre) polynomial by θ. Lambda represents the wavelength in the solvent. d is the particle size, r is the distance from the particle, m is the relative of the particle to the medium Complex refractive index. In addition, the refractive index of the solvent is n 0 When the refractive index of the particles is n, m=n/n 0 . Furthermore, coefficient A l (m, d) and B l (m, d) are given by the following formula. In the following expression,' is a derivative related to a factor in each function.
[ number 4]
[ number 5]
X is represented by the following formula. And, psi 1 (ρ) and ζ 1 (ρ) is represented by the following formula, in which J is a Bessel function and ζ is a Hankel function.
[ number 6]
[ number 7]
[ number 8]
< 1 st example of fitting >
Hereinafter, a description will be given of a fitting for obtaining the refractive index (real part of complex refractive index) and particle size distribution of a single particle. In the fitting, the refractive index (real part of complex refractive index) and the particle size distribution of the single type of particles were finally obtained using the number of particles as a variable.
For each scattering angleDegree actual measurement second-order autocorrelation function g (2) Preferably, the angle (τ) is two or more, but may be one angle. The number of scattering angles to be measured can be appropriately determined according to the number of variables required or the number of parameter-dependent data of the scattering intensity of the measurement parameter.
In the fitting, the initial particle number is set for each first-order autocorrelation function of the scattering angle by using the particle number as a variable in equation (1). A calculated value of a first-order autocorrelation function of formula (1) based on the set initial particle number is obtained. Determining a second-order autocorrelation function g from the calculated value of the first-order autocorrelation function (2) (τ)＝1+β·|g (1) (τ)| 2 Is a calculated value of (a). In addition, β is the device constant.
The difference between the value of the measured second-order autocorrelation function and the calculated value of the second-order autocorrelation function is obtained 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 referred to as the difference between the second-order autocorrelation function and the calculated value of the second-order autocorrelation function. The difference between the second-order autocorrelation functions is obtained for each scattering angle. The calculated value of the second-order autocorrelation function for each scattering angle corresponds to time-varying characteristic data of the scattering intensity of the measurement parameter calculated using a theoretical formula.
Actual measurement of total scattering intensity I for each scattering angle total . In the formula (2), the total scattering intensity I of the formula (2) based on the set initial particle number is obtained θ total Is a value of (2).
The measured total scattering intensity I shown in FIG. 3 was obtained for each scattering angle total The value of (2) and the total scattering intensity I of the formula (2) θ total Is a difference between calculated values of (a). In addition, the measured total scattering intensity I at any scattering angle total The value of (2) and the total scattering intensity I of the formula (2) θ total The difference between the calculated values of (2) is called the total scattering intensity I at the scattering angle total And (3) a difference. For total scattering intensity I total Obtaining the total scattering intensity I under the scattering angle total And (3) a difference. Total scattering intensity I of formula (2) θ total Corresponds to the measurement parameter calculated by the theoretical formulaIs dependent on the data.
Wherein when the calculated value of the second-order autocorrelation function is obtained using the formula (1) and when the calculated value of the total scattering intensity is obtained using the formula (2), the particle diameter in the dynamic light scattering of the formula (1) can be set to d DLS ) And (2) d (particle diameter in static light scattering is d SLS ) Ratio α=d SLS /d DLS For example, 0.78. Where α is a coefficient determined according to the structure of the particle.
In the fitting, the difference between the second-order autocorrelation function obtained for each scattering angle and the difference between the total scattering intensities at the scattering angles is used to obtain the final particle number and refractive index (real part of complex refractive index). For example, an evaluation value obtained by adding the value of the square of the difference between the second-order autocorrelation function obtained for each scattering angle and the value of the square of the difference between the total scattering intensities at the scattering angles is used for all the scattering angles. The particle number with the smallest evaluation value is taken as the final particle number.
Therefore, in the fitting, the number of particles and the relative complex refractive index m are repeatedly updated in the formulas (1) and (2) so that the evaluation value becomes minimum, and the final number of particles and the relative complex refractive index m are obtained. Then, the refractive index n of the particles is obtained from the relative complex refractive index m, assuming that the type of the solvent, that is, the refractive index, is known. The refractive index n of the particles obtained from the relative complex refractive index m is the real part of the complex refractive index.
In the fitting, the equation indicating the relative complex refractive index m is reflected, and in the equations (1) and (2), the values of the particle count and the relative complex refractive index m are updated, and the fitting of the actual measurement value and the calculated value is performed, thereby obtaining the final particle count and the relative complex refractive index m. The refractive index is fitted by a formula representing the relative complex refractive index m described above.
After setting initial values for the particle numbers of all particle diameters, the evaluation value is updated so as to be minimized. Thus, a histogram of particles can be obtained. I.e. by counting all d=d 0 ～d M N is obtained d C A particle size distribution can be obtained. This corresponds to step S16 described above.
The above step is a step of obtaining a particle size distribution of a single type of particles (step S16). The evaluation value for fitting is not limited to the above.
The optimization method of the fitting is not limited to the above, and for example, bayesian optimization can be used for the fitting.
Although the second-order autocorrelation function is used, the present invention is not limited to this, and a power spectrum may be used instead of the second-order autocorrelation function. Also, when the first-order autocorrelation function is actually measured by heterodyne detection, the first-order autocorrelation function may be used.
FIG. 3 is a graph showing an example of the relationship between scattering intensity and scattering angle of an aqueous dispersion of polystyrene particles having a particle diameter of 990 nm. FIG. 4 is a graph showing an example of a second-order autocorrelation function for each scattering angle, showing the dependence of the scattering angle of the second-order autocorrelation function for an aqueous dispersion of polystyrene particles having a particle diameter of 990 nm. In fig. 4, symbol 37 denotes a second-order autocorrelation function at a scattering angle of 50 °. Symbol 38 represents a second order autocorrelation function with a scattering angle of 90 °. Symbol 39 represents a second order autocorrelation function with a scattering angle of 140 °.
Fig. 5 is a graph showing calculated values of scattering angle and scattering intensity for each refractive index of particles having the same particle size, and shows a distribution of scattering intensity obtained by calculation. In fig. 5, reference numeral 40 denotes a distribution showing a relationship between a scattering angle and a scattering angle having a refractive index of 1.48. Reference numeral 41 denotes a distribution showing a relationship between a scattering angle and a scattering angle having a refractive index of 1.59. The symbol 42 is a distribution showing the relationship between the scattering angle and the scattering angle with a refractive index of 2.2. As shown in fig. 5, even for particles of the same particle size, the distribution of scattering intensity with respect to scattering angle varies with refractive index.
The refractive index n=1.59 and the particle diameter d=990 nm of polystyrene were obtained by the fitting described above. The refractive index n=1.59 is the real part of the complex refractive index.
The determination of the refractive index and particle diameter of polystyrene is shown by the above-mentioned fitting. In the formulas (1) and (2), the values of the particle count and the relative complex refractive index m are updated and the actual measurement value and the calculated value are fitted. The refractive index is fitted by a formula indicating the relative complex refractive index m. In this way, the final particle number and the relative complex refractive index m are obtained. The particle size distribution was obtained from the particle size at which the final particle number was obtained.
In addition to the scattering angle, in order to determine the wavelength dependence of the refractive index, a result of measurement at a different wavelength may be added. That is, the number of particle types, refractive index of each particle type, and particle size distribution may be obtained by measuring scattered light intensity for each of a plurality of measurement wavelengths using a plurality of measurement wavelengths of two or more wavelengths to obtain data of a plurality of scattered lights. In this case, the scattering angle may be one angle, or may be plural or 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 referred to as refractive index dispersion. When the measurement wavelength as the measurement parameter is changed, if the number of measurement wavelengths is plural, the number is not limited to two, but may be three or four.
Fig. 6 and 7 show the relationship between the scattering intensity and the measurement wavelength. FIG. 6 shows the calculated scattering intensity at a measurement wavelength of 488nm for two particles of different refractive index. As shown in fig. 6, the distribution 44 of the scattering intensity of the 1 st particle is different from the distribution 45 of the scattering intensity of the 2 nd particle.
Fig. 7 shows the calculated scattering intensity for two particles at the measurement wavelength of 632.8 nm. As shown in fig. 7, the distribution 46 of the scattering intensity of the 1 st particle is different from the distribution 47 of the scattering intensity of the 2 nd particle. As shown in fig. 6 and 7, the scattering intensity with respect to the measurement wavelength differs depending on the difference in refractive index of the particles.
For example, the parameter-dependent data of the scattering intensity of the dispersion liquid is obtained by calculating a time average value of the scattering intensity of the dispersion liquid for each laser beam wavelength, for example.
By increasing the number of measured wavelengths in addition to the scattering angle, a wavelength dependent signal of the refractive index can be obtained And (5) extinguishing. In this case, the refractive index N is determined by using a wavelength dependent formula such as Cauchy (Cauchy) formula n=d 1 +D 2 /λ 2 Similarly, the value D is obtained 1 And D 2 The refractive index N can also be obtained.
By using such an equation determined empirically or by a physical law, the number of parameters required for fitting can be reduced to reduce the amount of calculation of fitting when the number of measurement wavelengths is increased. This can shorten the time required for fitting, for example.
In addition, in addition to the theoretical formula, the time-varying characteristic data of the scattering intensity of the measurement parameter calculated by simulation and the parameter-dependent data of the scattering intensity of the measurement parameter calculated by simulation may be used in the fitting.
In the measurement step, the light intensity of the polarized component of scattered light of the dispersion obtained by irradiating the dispersion with measurement light of a specific polarization may be measured as the scattered intensity. The measurement step is performed by the scattered light measurement unit 14.
For example, a circularly polarized laser beam is irradiated to the dispersion Lq of the sample cell 16 as measurement light, and the polarization component of scattered light of the dispersion Lq is measured. Regarding the light intensity of the polarized component of scattered light, for example, the difference between the light intensity of vertically linearly polarized light and the light intensity of horizontally linearly polarized light is measured as the scattered intensity. In this case, when the scattering angle is changed and measured as in example 1 of the particle measurement method described above, a graph showing the relationship between scattering intensity and scattering angle shown in fig. 8 can be obtained. As shown in fig. 8, the distribution 48 of the scattering intensity of the spherical particles is different from the distribution 49 of the scattering intensity of the disk-shaped particles.
In addition, the vertically linearly polarized light means that the direction of linearly polarized light when the scattering surface is made horizontal is vertical. The horizontally linearly polarized light means that the direction of linearly polarized light when the scattering surface is made horizontal is horizontal.
In the measurement step, at least one of parameter-dependent data of the scattering intensity obtained by sequentially irradiating the dispersion with the plurality of polarized measurement lights and parameter-dependent data of the scattering intensity obtained by taking out the polarization components of the plurality of scattered lights emitted from the dispersion may be measured. The measurement step is performed by the scattered light measurement unit 14 and the polarizing element 28.
The parameter-dependent data of the scattering intensity obtained by sequentially irradiating the dispersion with the measurement light having a plurality of polarization states causes the measurement light to have a polarization state. The parameter-dependent data of the scattering intensity obtained by taking out the polarization components of the scattered light emitted from the dispersion liquid is data in which the polarization components of the scattered light are detected without bringing the measurement light into a polarization state. The data for detecting the polarization component of scattered light by bringing the measurement light into the polarization state is also included in the above-described parameter-dependent data for the scattered intensity.
For example, when polarized light is used, the polarization state of the measurement light is circularly polarized light, and the difference between the vertical polarized light intensity and the horizontal polarized light intensity can be used as the polarization component of the scattered light. For example, the polarization state of the measurement light is 45 ° linear polarized light, and the polarization component of the scattered light can be the sum of the vertical polarized light intensity and the horizontal polarized light intensity.
(example 2 of particle measurement apparatus)
Fig. 9 is a schematic diagram showing example 2 of a particle measurement apparatus according to an embodiment of the present invention.
In the particle measurement apparatus 60 shown in fig. 9, the same components as those of the particle measurement apparatus 10 shown in fig. 1 are denoted by the same reference numerals, and detailed description thereof is omitted.
The particle measurement apparatus 60 shown in fig. 9 is different from the particle measurement apparatus 10 shown in fig. 1 in that a white light source, an arrangement of optical elements, and the like are used.
The particle measurement apparatus 60 includes a light source 62, a beam splitter 64, a lens 65, and the sample cell 16. The light source 62, beam splitter 64, lens 65, and sample cell 16 are in a straight line L 1 And are arranged in series.
The light source unit 62 emits the incident light Ls, and a white light source can be used. As a white light source, for example, a Supercontinuum (SC) light source can be used.
The lens 65 is an objective lens that condenses the incident light Ls into the sample cell 16.
The beam splitter 64 has a transmissive and reflective surface 64a that transmits light incident from one direction and reflects light incident from the other direction. The beam splitter 64 is a cubic-shaped regular hexahedral beam splitter.
In the beam splitter 64, a straight line L is formed 1 Orthogonal 1 st axis C 11 A shutter 66, a lens 67, a pinhole 68, a lens 69, and a beam splitter 70 are arranged in series.
The beam splitter 70 has a transmissive and reflective surface 70a that transmits light incident from one direction and reflects light incident from the other direction. The beam splitter 70 is a cubic-shaped regular hexahedral beam splitter.
In the 1 st axis C, the lens 69 is not arranged on the surface 70b of the beam splitter 70 11 The upper is provided with a slit 71 and a mirror 72 in series. The opening 71a of the slit 71 is open to the surface 70 b. The light passing through the opening 71a of the slit 71 enters the mirror 72. There is also a diffraction grating 73 on which the reflected light reflected by the mirror 72 is incident.
The diffraction grating 73 is an optical element that splits incident light including scattered light into light of each wavelength by wavelength division. Scattered light of each wavelength can be obtained by the diffraction grating 73.
Further, there is provided a photodetector 74 on which the scattered light is incident by the diffraction grating 73, and the diffracted light obtained by diffraction according to wavelength. Scattered light whose wavelength is resolved by the photodetector 74 is detected for each wavelength. The photodetector 74 is connected to the arithmetic unit 18.
The photodetector 74 has a plurality of pixels, and detects the average time intensity and time dependence of the light intensity of each pixel. For example, a line camera in which photoelectric conversion elements are arranged on a straight line may be used for the photodetector 74. The photodetector 74 may be a photodetector in which a photomultiplier tube is arranged on a straight line instead of the line camera.
The mirror 72, the diffraction grating 73, and the photodetector 74 constitute a spectroscopic detection unit 80.
In relation to the sample cell 16, in relation to the 1 st axis C 11 Parallel 2 nd axis C 12 A shutter 75, a lens 76, a pinhole 77, a lens 78, and a mirror 79 are arranged in series.
The light reflected by the reflecting mirror 79 is incident on the face 70c of the beam splitter 70, and is reflected by the transmissive-reflective face 70a of the beam splitter 70 toward the reflecting mirror 72.
For example, electromagnetic shutters may be used as the shutter 66 and the shutter 75. The incidence of light to the beam splitter 70 is controlled by a shutter 66 and a shutter 75. By switching the shutter 66 and the shutter 75, either one of the light reflected by the sample cell 16 can be made incident on the beam splitter 70. When measuring two lights reflected by the sample cell 16, the shutter 66 and the shutter 75 are sequentially switched to perform measurement.
The pinholes 68 and 77 have a confocal function, and can pass only the component of light scattered at the focal point portion out of light scattered by the dispersion Lq through the pinholes. This can limit the measurement area of scattered light of the dispersion liquid Lq, and measurement can be performed without deteriorating the spatial coherence.
In the particle measurement apparatus 60, a supercontinuum light source is used as the light source 62. Light is irradiated from the light source 62 to the sample cell 16 through the beam splitter 64 and the lens 65. In the sample cell 16, the back-scattered light having a scattering angle of 180 ° returns to the beam splitter 64 again, enters the beam splitter 64 from the surface 64c of the beam splitter 64, is reflected by the transmissive/reflective surface 64a, and passes through the lens 67, the pinhole 68, and the lens 69. At this time, the shutter 66 is opened and the shutter 75 is closed.
As described above, the pinhole 68 has a confocal function, and only the component of the light scattered at the focal point portion among the light scattered by the dispersion Lq can pass through the pinhole 68. This can limit the measurement area of the scattered light in the sample cell 16, and can measure the scattered light without deteriorating the spatial coherence. Then, the beam splitter 70 is transmitted and passes through the slit 71, and is reflected by the mirror 72 in the spectroscopic detection unit 80, and enters the diffraction grating 73, and the scattered light reaching the photodetector 74 is detected by the photodetector 74. The scattered light is irradiated to different pixels for each wavelength through the diffraction grating 73, and is detected by spectroscopic detection. That is, scattered light is detected for each wavelength.
On the other hand, when scattered light reflected at 90 ° is measured in the sample cell 16, the scattered light passes through the lens 76, the pinhole 77, and the lens 78. At this time, the shutter 75 is opened, and the shutter 66 is closed. The scattered light is reflected by the reflecting mirror 79 onto the beam splitter 70, reflected by the transmissive/reflective surface 70a of the beam splitter 70, passes through the slit 71, is reflected by the reflecting mirror 72 onto the diffraction grating 73 in the spectroscopic detection unit 80, and further reaches the photodetector 74, where the scattered light is detected by the photodetector 74. In the particle measurement device 60, the intensity of scattered light having different scattering angles is measured for each wavelength in this manner. The particle measurement device 60 can measure the refractive index and the particle size distribution of a single type of particles contained in the dispersion liquid, similarly to the particle measurement device 10.
In the calculation unit 18, it is preferable that the refractive index of the single particle type obtained by the fitting is compared with the refractive index of the known material in a block (bulk) state, which is the refractive index when the known material is at 100% concentration, and the volume concentration of the constituent substance of the single particle type is calculated using the dependency of the refractive index on the volume concentration of the particle. The meaning of the volume concentration is the same as the volume density and the filling rate. The dependence of the refractive index means, for example, a linear change in refractive index with respect to bulk density.
The particle measurement method preferably further includes the steps of: and a step of comparing the refractive index of the single-type particles obtained with the refractive index of the known material at 100% concentration, and calculating the volume concentration of the constituent substance constituting the single-type particles obtained using the dependence of the refractive index on the volume concentration of the particles. By these steps, for example, the density of aggregates can be estimated from the obtained refractive index of the single particle.
The known material has a refractive index of 100% concentration, and the material is associated with the refractive index of the material at 100% concentration and stored in the calculation unit 18 as a library (library), for example.
(example 3 of particle measurement apparatus)
FIG. 10 is a schematic view showing example 3 of a particle measurement apparatus according to an embodiment of the present invention.
In the particle measurement apparatus 10a shown in fig. 10, the same components as those of the particle measurement apparatus 10 shown in fig. 1 are denoted by the same reference numerals, and detailed description thereof is omitted.
The particle measurement apparatus 10a shown in fig. 10 is different from the particle measurement apparatus 10 shown in fig. 1 in that the transmittance of the dispersion liquid Lq is measured, and a transmitted light measurement unit 90 for measuring the transmittance is provided. The transmitted light measuring unit 90 is connected to the calculating unit 18. The transmitted light measuring unit 90 may use a photomultiplier tube or a photodiode, for example.
In the particle measurement apparatus 10a, the transmitted light measurement section 90 is disposed opposite the polarizing element 28 through the sample cell 16 and on the optical axis C 1 And (3) upper part.
The transmitted light measuring unit 90 measures the light intensity of the transmitted light transmitted through the sample cell 16, and is not particularly limited to a photomultiplier tube as long as the light intensity of the transmitted light can be measured. The light intensity of the transmitted light obtained by the transmitted light measuring unit 90 is output to the calculating unit 18. The calculation unit 18 calculates the transmittance of the dispersion liquid Lq, and obtains transmittance data of the dispersion liquid Lq. The calculating unit 18 and the transmitted light measuring unit 90 constitute a transmittance measuring unit, and the transmittance measuring unit measures the transmittance of the dispersion Lq. The intensity of the light incident on the sample cell 16 is defined as I i The light intensity of the transmitted light transmitted through the sample cell 16 is defined as I o When the transmittance Ts is I o /I i . The transmittance Ts is represented by the following formula (3).
Ts＝exp(-τ a L) (3)
In the formula (3) of the transmittance Ts, τ a And L is the light absorption coefficient and L is the light path length. Absorption coefficient tau a Represented by the following formula (4). In the following formula (4), N is the number of particles (subscript d indicates a particle diameter d depending on the particle diameter).
C ext Is the extinction cross-sectional area (d is the particle diameter, m is the relative complex refractive index of the particles relative to the refractive index n0 of the solvent (m=n c /n 0 ): let the complex refractive index of the particles be n c =n+ik. ). The subscripts 0 to M of d are ordinals of the bins of the histogram of the particles shown in FIG. 11.
[ number 9]
In addition, extinction cross-sectional area C ext Represented by the following formula. Extinction cross-sectional area C ext A of (a) n 、b n Represented by the following formula. And, ψ n (ρ) and ζ n (ρ) is represented by the following formula.
[ number 10]
[ number 11]
[ number 12]
[ number 13]
[ number 14]
[ number 15]
Above mentionedWherein, ψ is n (ρ) and ζ n (ρ) is a Li Kadi-Bessel function. j (j) n (ρ) is a first class of ball Bessel function, h n (2) (ρ) is a second sphere Hanker function. And λ is the wavelength.
The calculation unit 18 of the particle measurement apparatus 10a calculates time-varying characteristic data of a plurality of scattering intensities of the measurement parameters and parameter-dependent data of a plurality of scattering intensities of the measurement parameters from the plurality of scattering intensity data obtained by the scattered light measurement unit 14, and fits the calculated time-varying characteristic data of a plurality of scattering intensities of the measurement parameters and the parameter-dependent data of a plurality of scattering intensities of the measurement parameters to the transmittance data of the dispersion liquid by using a theoretical formula based on a relationship between a predetermined complex refractive index, a particle diameter, and a scattering intensity, or a simulation of an electromagnetic wave behavior theory, and a theoretical formula based on a relationship between a predetermined complex refractive index, a particle diameter, and a transmittance, or a simulation of an electromagnetic wave behavior theory, to thereby calculate a complex refractive index and a particle diameter distribution of a single particle. The fitting will be described later.
In addition to the theoretical formula for specifying the relationship between the complex refractive index, the particle diameter, and the scattering intensity and the theoretical formula for specifying the relationship between the complex refractive index, the particle diameter, and the transmittance, the time-varying characteristic data of the scattering intensity of the measurement parameter calculated by the simulation based on the electromagnetic wave behavior theory and the parameter-dependent data and the transmittance data of the scattering intensity of the calculated measurement parameter may be used.
In the computing unit 18, the time-varying characteristic data of the scattering intensity of the calculated measurement parameter is calculated from a stokes-einstein theoretical formula. And, for example, parameter-dependent data of the scattering intensity is calculated from at least one of a Mie (Mie) scattering theory formula, a discrete dipole approximation method (DDA method), and a time-finite difference method (FDTD method). In addition, the discrete dipole approximation method (DDA method) and the time-finite difference method (FDTD method) correspond to simulations based on the theory of electromagnetic wave behavior. The method equivalent to the simulation based on the electromagnetic wave behavior theory can be appropriately utilized, and is not particularly limited to the discrete dipole approximation method (DDA method) and the time-finite difference method (FDTD method) described above.
The theoretical formula is not particularly limited to the above formula, and various theoretical formulas such as scattering theory can be appropriately used.
In addition, in the simulation based on the electromagnetic wave behavior theory related to the complex refractive index, the particle diameter, and the transmittance, for example, the Mie (Mie) scattering theory formula, the discrete dipole approximation method (DDA method), and the finite difference in time domain method (FDTD method) can be used as in the simulation based on the electromagnetic wave behavior theory related to the complex refractive index, the particle diameter, and the scattering intensity.
The transmittance of the dispersion liquid Lq is not limited to that measured by the particle measuring device 10a, and a previously measured transmittance of the dispersion liquid Lq may be used. Therefore, in the particle measurement apparatus 10 shown in fig. 1, the complex refractive index can be obtained as in the particle measurement apparatus 10 a.
(example 2 of particle measurement method)
Fig. 12 is a flowchart showing example 2 of a method for measuring particles according to an embodiment of the present invention.
The difference of example 2 in the particle measurement method is that the complex refractive index is obtained using the scattering intensity of the dispersion, as compared with example 1 in the particle measurement method.
The difference of example 2 in the particle measurement method is that the complex refractive index composed of the real part and the imaginary part is obtained using the transmittance of the dispersion liquid, as compared with example 1 in the particle measurement method. The transmittance of the dispersion may be measured before or after the measurement of the scattering intensity of the dispersion to be measured. Further, if the transmittance of the dispersion is known, the known transmittance can be used.
As shown in fig. 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). By the optimization step (step S24), the analysis result (step S26), that is, the complex refractive index and the particle diameter distribution of the single type of particles (step S26) can be obtained.
In the measurement step (step S20), for example, the scattering angle dependence of the temporal fluctuation of the scattering intensity and the temporal average value of the scattering intensity and the transmittance of the dispersion are measured.
In the step of obtaining experimental data (step S22), for example, an autocorrelation function of the scattering intensity with respect to time fluctuation is obtained from the measurement value in the measurement step (step S20). And, a time average value of the scattering angle-dependent or wavelength-dependent scattering intensity of the time average value of the scattering intensity is obtained. Then, the transmittance of the dispersion was measured to obtain transmittance data. Thus, for example, the scattering intensity for each scattering angle shown in fig. 3 can be obtained. Further, the transmittance of the dispersion can be obtained. The timing of obtaining the transmittance data may be the measurement step (step S20). However, since the transmittance data is only required when fitting, the step of obtaining the transmittance data may be performed before fitting, that is, before the step of obtaining the complex refractive index and the particle size distribution of the single particle. Further, since the known transmittance data can be used if the transmittance data is known, a step of obtaining the transmittance data is not necessarily required.
In the optimization step (step S24), for example, a theoretical formula of the autocorrelation function and the scattering intensity and the transmittance of the dispersion liquid is fitted to the time-averaged value of the autocorrelation function and the scattering intensity of the temporal fluctuation of the scattering intensity obtained in step S22 and the transmittance of the dispersion liquid. In step S24, after an initial value is set for the particle number of the particle size of the single particle, the final particle number is obtained by updating the evaluation value to be the smallest. In addition, the initial value is set by generating a random variable.
Hereinafter, the method for measuring particles including fitting will be described in detail.
First, for example, a laser beam having a wavelength of 488nm is irradiated from the 2 nd light source unit 22 shown in fig. 10 to the dispersion Lq. The scattered light scattered by the irradiation is detected by the photodetector 34 for a predetermined time at a predetermined scattering angle. This can obtain the scattering intensity of the dispersion Lq at the scattering angle. The transmitted light transmitted through the dispersion Lq by the laser beam is also measured by the transmitted light measuring unit 90.
Then, the scattered light measuring unit 14 is rotated by the rotating unit 36 to change the scattering angle θ, thereby obtaining the scattering intensity of the dispersion liquid Lq. The scattering intensity of the dispersion Lq was measured by repeating the change of the scattering angle and the measurement of the scattering intensity of the dispersion Lq. The scattering angle is two or more, and the scattering intensity is measured every 5 ° from 30 ° to 160 °. The above steps are measurement steps, and correspond to step S20 described above.
Next, the calculating unit 18 calculates time-varying characteristic data of the scattering intensity from the time-dependence of the scattering intensity of the dispersion Lq obtained in the measuring step. The time-varying characteristic data of the scattering intensity is 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-varying characteristic data of the scattering intensity is obtained for each scattering angle. That is, there are a plurality of time varying data.
The calculation unit 18 calculates the transmittance of the dispersion liquid Lq from the above equation based on the light intensity of the laser beam and the light intensity of the transmitted light transmitted through the dispersion liquid Lq. In addition, when the wavelength of the laser beam is changed, transmittance can be obtained for each wavelength of the laser beam. That is, wavelength dependent data of transmittance can be obtained.
Next, the calculating unit 18 calculates parameter-dependent data of the scattering intensity from the scattering intensity of the dispersion liquid obtained in the measuring step.
The parameter-dependent data of the scattering intensity of the dispersion liquid is obtained by calculating, for example, a time average value of the scattering intensity of the dispersion liquid for each scattering angle. Thus, for example, data of the scattering intensity for each scattering angle as shown in fig. 3 is obtained.
The step of calculating the time-varying 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 as described above is a calculating step, and corresponds to step S22 described above.
Next, the calculation unit 18 uses a theoretical formula or simulation of electromagnetic wave behavior theory based on a relationship between a predetermined complex refractive index, particle diameter, and scattering intensity, and a theoretical formula or simulation of electromagnetic wave behavior theory based on a relationship between a predetermined complex refractive index, particle diameter, and transmittance to fit time-varying characteristic data of scattering intensity at least one scattering angle, parameter-dependent data of scattering intensity at a plurality of scattering angles, and transmittance data of the dispersion. By this fitting, the complex refractive index and the particle size distribution of the single type of particles were obtained. This corresponds to steps S24 and S26 described above. The theoretical formula defining the relationship between the complex refractive index, the particle diameter and the transmittance is, for example, the absorbance τ of the above formula (4) a Is a formula (I).
As described above, one kind of particles is contained in the dispersion.
As described above, the first order autocorrelation function is defined by g (1) (τ)＝exp(-Dq 2 τ) represents. The relationship between the diffusion coefficient and the particle size obtained from the autocorrelation function is applicable to stokes-einstein's formula for a general dynamic light scattering method.
When the particles have a particle size distribution, the first-order autocorrelation function is represented by the above formula (1). The scattering intensity is expressed by the following formula (2). Formulas (1) and (2) above and below are theoretical formulas, I of formulas (1) and (2) θ total Are all calculated values.
< 2 nd example of fitting >
The fitting to determine the complex refractive index and the particle size distribution of a single particle will be described below. In the fitting, the complex refractive index and the particle size distribution of the single particle type are finally obtained using the number of particles as a variable.
Measuring a second-order autocorrelation function g for each scattering angle (2) Preferably, the angle (τ) is two or more, but may be one angle. The number of scattering angles to be measured can be appropriately determined according to the number of variables required or the number of parameter-dependent data of the scattering intensity of the measurement parameter.
In the fitting, a first order autocorrelation function for each scatter angleThe initial particle number is set in equation (1) using the particle number as a variable. A calculated value of a first-order autocorrelation function of formula (1) based on the set initial particle number is obtained. Determining a second-order autocorrelation function g from the calculated value of the first-order autocorrelation function (2) (τ)＝1+β·|g (1) (τ)| 2 Is a calculated value of (a). In addition, β is the device constant.
The difference between the value of the measured second-order autocorrelation function and the calculated value of the second-order autocorrelation function is obtained 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 referred to as the difference between the second-order autocorrelation function and the calculated value of the second-order autocorrelation function. The difference between the second-order autocorrelation functions is obtained for each scattering angle. The calculated value of the second-order autocorrelation function for each scattering angle corresponds to time-varying characteristic data of the scattering intensity of the measurement parameter calculated using a theoretical formula.
Actual measurement of total scattering intensity I for each scattering angle total . In the formula (2), the total scattering intensity I of the formula (2) based on the set initial particle number is obtained θ total Is a value of (2).
The measured total scattering intensity I shown in FIG. 3 was obtained for each scattering angle total The value of (2) and the total scattering intensity I of the formula (2) θ total Is a difference between calculated values of (a). In addition, the measured total scattering intensity I at any scattering angle total The value of (2) and the total scattering intensity I of the formula (2) θ total The difference between the calculated values of (2) is called the total scattering intensity I at the scattering angle total And (3) a difference. For total scattering intensity I total Obtaining the total scattering intensity I under the scattering angle total And (3) a difference. Total scattering intensity I of formula (2) θ total The calculated value of (2) corresponds to the parameter dependent data of the scattering intensity of the measurement parameter calculated by the theoretical formula.
Determining the measured transmittance value and ts=exp (- τ) of formula (3) a L) the difference between calculated values of the transmittance Ts. The difference between the measured transmittance value and the calculated transmittance value Ts is referred to as the transmittance difference.
In the fitting, the difference between the second-order autocorrelation function obtained for each scattering angle and the difference between the total scattering intensity and the transmittance at the scattering angle is used to obtain the final particle number and refractive index. For example, an evaluation value obtained by adding, for all scattering angles, a value obtained by summing the value of the square of the difference between the second-order autocorrelation function obtained for each scattering angle and the value of the square of the difference between the total scattering intensities at the scattering angles and the value of the square of the difference between the transmittances is used. The particle number with the smallest evaluation value is taken as the final particle number.
Therefore, in the fitting, the number of particles and the relative complex refractive index m are repeatedly updated in the formulas (1) (2) and (4) so that the evaluation value becomes minimum, and the final number of particles and the relative complex refractive index m are obtained. Then, the refractive index n of the particles is obtained from the relative complex refractive index m, assuming that the type of the solvent, that is, the refractive index, is known.
In the fitting, the equation indicating the relative complex refractive index m is reflected, and in the equations (1), (2) and (4), the values of the particle count and the relative complex refractive index m are updated and the fitting of the measured value and the calculated value is performed, thereby obtaining the final particle count and the relative complex refractive index m. The complex refractive index is fitted by a formula representing the relative complex refractive index m described above.
After setting initial values for the particle numbers of all particle diameters, the evaluation value is updated so as to be minimized. Thus, a histogram of particles can be obtained. I.e. by counting all d=d 0 ～d M N is obtained d C A particle size distribution can be obtained. This corresponds to step S26 described above.
The above step is a step of obtaining a particle size distribution of a single type of particles (step S26). The evaluation value for fitting is not limited to the above.
The optimization method of the fitting is not limited to the above, and for example, bayesian optimization can be used for the fitting.
Although the second-order autocorrelation function is used, the present invention is not limited to this, and a power spectrum may be used instead of the second-order autocorrelation function. Also, when the first-order autocorrelation function is actually measured by heterodyne detection, the first-order autocorrelation function may be used.
In addition to the scattering angle, in order to determine the wavelength dependence of the complex refractive index, it is also possible to add the results of measurement at different wavelengths. That is, the scattered light intensities are measured for each of the plurality of measurement wavelengths using a plurality of measurement wavelengths of two or more wavelengths, and data of a plurality of scattered lights are obtained. The transmittance is measured using a plurality of measurement wavelengths of two or more wavelengths to obtain the transmittance for each measurement wavelength. The number of particle types, the complex refractive index of each particle type, and the particle size distribution can also be obtained. In this case, the scattering angle may be one angle, or may be plural 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 referred to as refractive index dispersion. When the measurement wavelength as the measurement parameter is changed, if the number of measurement wavelengths is plural, the number is not limited to two, but may be three or four.
Furthermore, the volume concentration of the dispersion can be used for fitting.
In this case, the calculation unit 18 can determine the particle size distribution of the complex refractive index and the number concentration of the single particle by fitting using the time-varying 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 liquid. Here, the volume concentration data of the dispersion means data indicating the volume concentration of the dispersion, and the volume concentration Φ is represented by the following formula. In the formula of the volume concentration phi, d is the particle diameter.
The particle size distribution of the number concentration is a distribution of the number of particles per unit volume of the dispersion relative to the particle size. N (N) d The number of particles per unit volume of the dispersion.
[ number 16]
When the volume concentration of the dispersion is known, the difference between the value of the volume concentration and the calculated value of the volume concentration phi represented by the following formula is obtained. The difference between the measured value of the volume concentration and the calculated value of the volume concentration phi is referred to as the difference between the volume concentrations. The known value of the volume concentration is, for example, a measured value.
As a method for obtaining the volume concentration of the dispersion, for example, the following methods are available: the particles in the dispersion were centrifugally precipitated, the weight of the particles was measured, the weight of the dispersion medium was calculated, and the volume concentration of the dispersion liquid was determined from the known specific gravities of the particles and the dispersion medium.
In the fitting, the difference between the second-order autocorrelation function obtained for each scattering angle and the difference between the total scattering intensities at the scattering angles, the difference in transmittance, and the difference in volume concentration are used to obtain the final particle number and the complex refractive index. For example, an evaluation value obtained by adding, for all scattering angles, a value obtained by summing the value of the square of the difference between the second-order autocorrelation function obtained for each scattering angle and the value of the square of the difference between the total scattering intensities at the scattering angles, a value of the square of the difference between the transmittances, and a value of the square of the difference between the volume concentrations is used. The particle number with the smallest evaluation value is taken as the final particle number. In this case, the number of particles can be obtained in the form of a number concentration. Thus, the number of particles in the dispersion can be obtained in absolute value.
(example 4 of particle measurement apparatus)
FIG. 13 is a schematic view showing example 4 of a particle measurement apparatus according to an embodiment of the present invention.
In the particle measurement apparatus 60a shown in fig. 13, the same components as those of the particle measurement apparatus 60 shown in fig. 9 are denoted by the same reference numerals, and detailed description thereof is omitted.
The particle measuring apparatus 60a shown in fig. 13 is different from the particle measuring apparatus 60 shown in fig. 9 in that the transmittance of the dispersion liquid Lq is measured, and a transmitted light measuring section 90 for measuring the transmittance is provided. The transmitted light measuring section 90 is disposed so as to face the lens 65 through the sample cell 16.
Although not shown, the transmitted light measuring unit 90 is connected to the calculating unit 18. The calculation unit 18 and the transmitted light measurement unit 90 constitute a transmittance measurement unit, as in the case of the particle measurement apparatus 10a shown in fig. 10. The transmittance of the dispersion Lq is measured by a transmittance measuring unit. The transmitted light measuring section 90 has the same structure as the particle measuring apparatus 10a shown in fig. 10, and may be a photomultiplier tube or a photodiode, for example. The complex refractive index can be obtained using the measuring device 60 a.
The transmittance of the dispersion Lq is not limited to the refractive index measured by the particle measuring device 60a, and a predetermined transmittance of the dispersion Lq may be used. Therefore, in the particle measurement apparatus 60 shown in fig. 9, the complex refractive index can be obtained as in the particle measurement apparatus 60 a.
The present invention is basically constructed as described above. While the particle measurement apparatus and the particle measurement method according to the present invention have been described in detail above, the present invention is not limited to the above-described embodiments, and various modifications and alterations are of course possible within the scope of the present invention.
Example 1
The features of the present invention will be described in more detail below with reference to examples. The materials, reagents, amounts of materials, proportions thereof, operations and the like shown in the following examples may be appropriately modified without departing from the spirit of the present invention. Accordingly, the scope of the present invention is not limited to the following examples.
In this example, the dynamic light scattering measurement of the dispersion containing particles was performed using the scattering angle as the measurement parameter. The following samples 1 and 2 were used as the dispersion liquid.
Sample 1 was an aqueous dispersion of polystyrene particles and pure water was used as a solvent and polystyrene particles were used as particles. The polystyrene particles had a 1 st particle diameter of 990nm. The primary particle diameter of the polystyrene particles is a table of contents.
Sample 2 was an aqueous dispersion of titanium oxide particles and pure water was used as the solvent. The primary particle diameter of the titanium oxide particles is 30 to 50nm. The 1 st particle diameter of the titanium oxide particles is a directory value.
In addition, the concentration of the particles of sample 1 was 4×10 -4 Mass%. Sample 2 had a particle concentration of 4X 10 -3 Mass%.
The time-average intensity of scattered light was measured at every 5 ° for the scattering angle from 30 ° to 160 ° using a laser beam having a wavelength of 633nm, and the time-dependent data were measured at the scattering angles of 50 °, 90 ° and 140 °. The scattered light intensity at each scattering angle is measured to determine an autocorrelation function, and a theoretical formula is fitted to the autocorrelation function to determine the refractive index and particle size distribution of the particles.
Here, fig. 14 is a graph showing a particle size distribution of polystyrene particles, fig. 15 is a graph showing a relationship between scattering intensity and scattering angle of polystyrene particles, and fig. 16 is a graph showing a second-order autocorrelation function of polystyrene particles.
For sample 1, the particle size distribution shown in fig. 14 was obtained. Further, a refractive index of 1.56 was obtained. Regarding fitting, as described above. The above equation representing the relative complex refractive index m is reflected, and the values of the particle count and the relative complex refractive index m are updated in the above equations (1) and (2), and the actual measurement value and the calculated value are fitted. The refractive index is fitted by a formula indicating the relative complex refractive index m. In this way, the final particle number and the relative complex refractive index m are obtained. The particle size distribution is obtained from the final particle count.
The fitting result of sample 1 was discussed. As shown in fig. 15, the distribution 50 indicating the measured value coincides with the distribution 51 based on fitting with respect to the scattering intensity. The distribution 51 is a calculated value based on the above formula (2).
As shown in fig. 16, the distribution 52 representing the measured value matches the distribution 53 based on the fitting, with respect to the second-order autocorrelation function.
In addition, the second-order autocorrelation function passes through g as described above (2) (τ)＝1+β·|g (1) (τ)| 2 Calculations were performed.
In this way, in sample 1, the convergence of the solution based on the fitting also proceeds correctly. From the obtained particle size distribution, it was also found that the particles were monodisperse in water at 1 particle size and that the refractive index was also a condition that could be accurately measured.
Here, fig. 17 is a graph showing the particle size distribution of the titanium oxide particles, fig. 18 is a graph showing the relationship between the scattering intensity and the scattering angle of the titanium oxide particles, and fig. 19 is a graph showing the second-order autocorrelation function of the titanium oxide particles.
For sample 2, the particle size distribution shown in fig. 17 was obtained. Further, a refractive index of 2.28 was obtained.
The fitting result for sample 2 was discussed. As shown in fig. 18, with respect to the scattering intensity, a distribution 54 representing the measured value coincides with a distribution 55 based on fitting.
As shown in fig. 19, the distribution 56 representing the measured value matches the distribution 57 based on the fitting, with respect to the second-order autocorrelation function.
In addition, the second-order autocorrelation function passes through g as described above (2) (τ)＝1+β·|g (1) (τ)| 2 Calculations were performed.
In this way, in sample 2, the convergence of the solution based on the fitting also proceeds correctly. Further, it was found that the particle size distribution was 300nm and was large, and that the particles were aggregated, and the refractive index of the obtained aggregate of nanoparticles was the refractive index.
In addition, regarding fitting, as described above. The above equation representing the relative complex refractive index m is reflected, and the values of the particle count and the relative complex refractive index m are updated in the above equations (1) and (2), and the actual measurement value and the calculated value are fitted. The refractive index is fitted by a formula indicating the relative complex refractive index m. In this way, the final particle number and the relative complex refractive index m are obtained. The particle size distribution is obtained from the final particle count.
The rutile type of titanium oxide used in sample 2 generally has a refractive index of 2.7. Since the aggregate is composed of water having a refractive index of 1.3 and titanium oxide in volume, assuming that the refractive index changes linearly with respect to the volume density, it can be estimated that the refractive index is 2.4 when the filling rate of titanium oxide is 74% and the refractive index is about 2.28 when the filling rate is 70% in the close-packed structure. Thus, the density of the aggregates can be estimated from the refractive index. An effective medium approximation (EMA: effective media approximation) can be used in the calculation of the refractive index.
Example 2
In this example, the dynamic light scattering measurement of the dispersion containing particles was performed using the scattering angle as the measurement parameter. The following sample 3 was used as the dispersion liquid.
Sample 3 used a single dispersion in which Pigment Red 254 was dispersed in a dispersion medium.
The dispersion medium used an organic solvent having a refractive index of 1.4.
The measurement wavelength of the scattering intensity was 488nm. The measurement wavelength of the transmittance was 488nm, and the measurement optical path length of the transmittance was 10mm.
The time-average intensity of scattered light was measured at a scattering angle of 30 ° to 160 ° (step size of 10 °) using a laser beam having a wavelength of 488nm, and time-dependent data were measured at scattering angles of 50 °, 90 ° and 150 °. The autocorrelation function was obtained by measuring the scattered light intensity at each scattering angle.
Then, the light intensity of the transmitted light was measured using a laser beam having a wavelength of 488nm as the incident light, and the transmittance was obtained. The intensity of the incident light is known.
The complex refractive index and particle size distribution of the particles were determined by fitting the theoretical formula to the autocorrelation function, scattering intensity and transmittance.
Here, fig. 20 is a graph showing the particle size distribution of sample 3. Fig. 21 is a graph showing the relationship between the scattering intensity and the scattering angle of sample 3. Fig. 22 is a graph showing the second-order autocorrelation function of sample 3 at a scattering angle of 50 °, fig. 23 is a graph showing the second-order autocorrelation function of sample 3 at a scattering angle of 90 °, and fig. 24 is a graph showing the second-order autocorrelation function of sample 3 at a scattering angle of 150 °. Fig. 25 is a graph showing the transmittance of sample 3.
For sample 3, the particle size distribution shown in fig. 20 was obtained. Further, the complex refractive index of sample 3 was 1.61+0.19i.
Regarding fitting, as described above. The values of the particle count and the relative complex refractive index m are updated in the above-described formulas (1), (2) and (4) to fit the actual measurement value and the calculated value. The refractive index is fitted by a formula indicating the relative complex refractive index m. In this way, the final particle number and the relative complex refractive index m are obtained. The particle size distribution shown in fig. 20 was obtained from the final particle count. The complex refractive index of the particles is obtained from the relative complex refractive index m. The complex refractive index contains not only a real part but also an imaginary part.
The fitting result of sample 3 was discussed. As shown in fig. 21, the distribution 100 representing the measured value coincides with the distribution 101 based on fitting with respect to the scattering intensity. The distribution 101 is a calculated value based on the above formula (2).
As shown in fig. 22, the distribution 102 indicating the actual measurement value matches the distribution 103 based on fitting with respect to the second-order autocorrelation function at the scattering angle of 50 °.
As shown in fig. 23, with respect to the second-order autocorrelation function at the scattering angle 90 °, the distribution 104 representing the measured value coincides with the distribution 105 based on fitting.
As shown in fig. 24, with respect to the second-order autocorrelation function at the scattering angle 150 °, the distribution 106 representing the measured value coincides with the fitting-based distribution 107.
In addition, the second-order autocorrelation function passes through g as described above (2) (τ)＝1+β·|g (1) (τ)| 2 Calculations were performed.
As shown in fig. 25, regarding the transmittance, the measured value 108 coincides with the fitting-based value 109. The actual measurement value 108 is a calculation value based on the formula (3).
In this way, in sample 3, the convergence of the solution based on the fitting also proceeds correctly. From the obtained particle size distribution, it was found that the particles were monodisperse in a dispersion medium at 1 particle size, and that the complex refractive index was also a condition under which accurate measurement was possible.
Symbol description
10-particle measuring apparatus, 12-incidence setting unit, 13-parameter setting unit, 14-scattered light measuring unit, 16-sample cell, 18-calculating unit, 20-1 st light source unit, 21 a-1 st shutter, 21 b-2 nd shutter, 22-2 nd light source unit, 24-half mirror, 26, 32-condensing lens, 28, 30-polarizing element, 34-light detecting unit, 36-rotating unit, 37, 38, 39-second order autocorrelation function, 40, 41, 42, 44, 45, 46, 47, 48-distribution, 50, 51, 52, 53, 54, 55, 56, 57-distribution, 60-particle measuring apparatus, 62-light source section, 64, 70-beam splitter, 64a, 70 a-transflective surface, 64C, 70b, 70C-surface, 65, 67, 69, 76, 78-lens, 66, 75-shutter, 68, 77-pinhole, 71-slit, 71 a-opening, 72, 79-mirror, 73-diffraction grating, 74-photodetector, 80-spectroscopic detection section, 90-transmitted light measuring section, 100, 101, 102, 103, 104, 105-distribution, 106, 107-distribution, 108-measured value, 109-based on the fitted value, C 1 -optical axis, C 11 -1 st axis, C 12 -2 nd axis, L 1 -straight line, lq-dispersion, ls-incident light, θ -scattering angle.
Claims (20)
1. A particle measurement device for measuring particles comprising a dispersion of a single type of particles, comprising:
a light source unit that irradiates the dispersion with measurement light;
a parameter setting unit that sets at least one of a scattering angle and a measurement wavelength as a measurement parameter;
a scattered light measurement unit that obtains a plurality of pieces of scattered intensity data by repeatedly changing the value of the measurement parameter set by the parameter setting unit and repeatedly measuring the scattered intensity of scattered light emitted from the dispersion by the measurement light; and
And a calculation unit that calculates time-varying characteristic data of scattering intensity and parameter-dependent data of scattering intensity from the plurality of scattering intensity data obtained by the scattered light measurement unit, and calculates a refractive index and a particle diameter distribution of the single particle by fitting the calculated time-varying characteristic data of scattering intensity and the parameter-dependent data of scattering intensity by using a theoretical formula or a simulation based on electromagnetic wave behavior theory that defines a relationship between refractive index, particle diameter and scattering intensity.
2. A particle measurement device for measuring particles comprising a dispersion of a single type of particles, comprising:
a light source unit that irradiates the dispersion with measurement light;
a parameter setting unit that sets at least one of a scattering angle and a measurement wavelength as a measurement parameter;
a scattered light measurement unit that obtains a plurality of pieces of scattered intensity data by repeatedly changing the value of the measurement parameter set by the parameter setting unit and repeatedly measuring the scattered intensity of scattered light emitted from the dispersion by the measurement light; and
And a calculation unit that calculates time-varying characteristic data of scattering intensity and parameter-dependent data of scattering intensity from the plurality of scattering intensity data obtained by the scattered light measurement unit, and calculates a complex refractive index and a particle diameter distribution of the single particle by fitting the calculated time-varying characteristic data of scattering intensity, the parameter-dependent data of scattering intensity, and the transmittance data of the dispersion using a theoretical formula or simulation based on electromagnetic wave behavior theory that defines a relationship between complex refractive index and particle diameter and scattering intensity, and a theoretical formula or simulation based on electromagnetic wave behavior theory that defines a relationship between complex refractive index and particle diameter and transmittance.
3. The particle measurement apparatus according to claim 2, wherein,
the measuring device has a transmittance measuring unit for measuring the transmittance of the dispersion liquid.
4. The particle measurement device according to any one of claim 1 to 3, wherein,
the measurement parameter is the scattering angle, and the scattered light measurement unit changes the value of the scattering angle to two or more angles and measures the scattering intensity of the scattered light of the dispersion liquid for each of a plurality of scattering angles to obtain a plurality of scattering intensity data.
5. The particle measurement device according to any one of claim 1 to 3, wherein,
the measurement parameter is the measurement wavelength, and the scattered light measurement unit obtains a plurality of pieces of scattered intensity data by measuring the scattered intensity of the scattered light of the dispersion liquid for each of a plurality of measurement wavelengths using the measurement wavelengths of two or more wavelengths.
6. The particle measurement device according to any one of claim 1 to 3, wherein,
the scattered light measurement unit measures, as the scattered intensity, the light intensity of a polarized component of the scattered light of the dispersion obtained by irradiating the dispersion with the measurement light that is the specific polarized light.
7. The particle measurement device according to any one of claim 1 to 3, wherein,
the scattered light measurement unit measures at least one of parameter-dependent data of scattered intensity obtained by sequentially irradiating the dispersion with the measurement light in a plurality of polarization states and parameter-dependent data of scattered intensity obtained by taking out the polarization components of the scattered light emitted from the dispersion.
8. The particle measurement device according to any one of claim 1 to 3, wherein,
the calculated time-varying characteristic data of the scattering intensity of the measurement parameter is data calculated according to a stokes-einstein theoretical formula, and the parameter-dependent data of the scattering intensity of the measurement parameter is data calculated according to at least one of a mie scattering theoretical formula, a discrete dipole approximation method, and a time domain finite difference method.
9. The particle measurement apparatus according to claim 1, wherein,
the calculation unit compares the refractive index of the single-type particles obtained with the refractive index of the known material at 100% concentration, and calculates the volume concentration of the constituent substance constituting the single-type particles obtained using the dependence of the refractive index on the volume concentration of the particles.
10. The particle measurement apparatus according to claim 2, wherein,
the calculation unit calculates a particle size distribution of complex refractive index and number concentration of the single particle by fitting using the time-varying 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 liquid.
11. A method for measuring particles, which is a method for measuring particles comprising a dispersion of particles of a single type, wherein,
at least one of the scattering angle and the measurement wavelength is set as a measurement parameter,
the measuring method comprises the following steps:
a measurement step of changing the set value of the measurement parameter a plurality of times to measure a scattering intensity of scattered light emitted from the dispersion liquid by the measurement light a plurality of times;
a calculation step of calculating time-varying characteristic data of the scattering intensity and parameter-dependent data of the scattering intensity from the plurality of scattering intensity data obtained in the measurement step;
fitting time variation characteristic data of the scattering intensity and parameter dependent data of the scattering intensity obtained by the calculating step by using a theoretical formula or simulation based on an electromagnetic wave behavior theory in which a relation between refractive index, particle diameter and scattering intensity is defined; and
And determining the refractive index and the particle size distribution of the single particle in the dispersion.
12. A method for measuring particles, which is a method for measuring particles comprising a dispersion of particles of a single type, wherein,
at least one of the scattering angle and the measurement wavelength is set as a measurement parameter,
the measuring method comprises the following steps:
a measurement step of changing the set value of the measurement parameter a plurality of times to measure a scattering intensity of scattered light emitted from the dispersion liquid by the measurement light a plurality of times;
a calculation step of calculating time-varying characteristic data of the scattering intensity and parameter-dependent data of the scattering intensity from the plurality of scattering intensity data obtained in the measurement step; and
And a step of obtaining the complex refractive index and the particle size distribution of the single particle by fitting the transmittance data of the dispersion, the time-varying characteristic data of the scattering intensity obtained in the calculation step, and the parameter-dependent data of the scattering intensity, using a theoretical formula or simulation of an electromagnetic wave behavior theory based on a relationship between the complex refractive index and the particle size and the scattering intensity, and a theoretical formula or simulation of an electromagnetic wave behavior theory based on a relationship between the complex refractive index and the particle size and the transmittance.
13. The method for measuring particles according to claim 12, wherein,
the measurement method includes a step of measuring the transmittance of the dispersion liquid to obtain the transmittance data.
14. The method for measuring particles according to any one of claims 11 to 13, wherein,
the measured parameter is the scattering angle,
in the measuring step, the scattering intensity of the scattered light of the dispersion is measured for each of a plurality of scattering angles by changing the value of the scattering angle to two or more angles.
15. The method for measuring particles according to any one of claims 11 to 13, wherein,
the measurement parameter is the measurement wavelength, and in the measurement step, the scattering intensity of the scattered light of the dispersion is measured for each of a plurality of measurement wavelengths using the measurement wavelengths of two or more wavelengths.
16. The method for measuring particles according to any one of claims 11 to 13, wherein,
in the measuring step, the light intensity of the polarized component of scattered light of the dispersion obtained by irradiating the dispersion with the measuring light as the specific polarized light is measured as the scattered intensity.
17. The method for measuring particles according to any one of claims 11 to 13, wherein,
in the measuring step, at least one of parameter-dependent data of scattering intensity obtained by sequentially irradiating the dispersion with the measurement light in a plurality of polarization states and parameter-dependent data of scattering intensity obtained by taking out the polarization components of the scattered light emitted from the dispersion are measured.
18. The method for measuring particles according to any one of claims 11 to 13, wherein,
the calculated time-varying characteristic data of the scattering intensity of the measurement parameter is data calculated according to a stokes-einstein theoretical formula, and the parameter-dependent data of the scattering intensity of the measurement parameter is data calculated according to at least one of a mie scattering theoretical formula, a discrete dipole approximation method, and a time domain finite difference method.
19. The method for measuring particles according to claim 11, wherein,
the measurement method further comprises the following steps: and a step of comparing the refractive index of the single-type particles obtained with the refractive index of the known material at 100% concentration, and calculating the volume concentration of the constituent substance constituting the single-type particles obtained using the dependence of the refractive index on the volume concentration of the particles.
20. The method for measuring particles according to claim 12, wherein,
the particle size distribution of the complex refractive index and the number concentration of the single particle is obtained by fitting using the time-varying characteristic data of the scattering intensity and the parameter-dependent data of the scattering intensity, the transmittance data, and the volume concentration data of the dispersion liquid.
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| JP2021-102668 | 2021-06-21 | ||
| JP2021-194045 | 2021-11-30 | ||
| JP2021194045 | 2021-11-30 | ||
| PCT/JP2022/021361 WO2022270204A1 (en) | 2021-06-21 | 2022-05-25 | Particle measurement device and particle measurement method |
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| CN117501094A true CN117501094A (en) | 2024-02-02 |
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| CN202280042838.XA Pending CN117501094A (en) | 2021-06-21 | 2022-05-25 | Particle measurement device and particle measurement method |
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