Method for Measuring Concentration of Hollow Particles

Abstract

To provide a hollow particle concentration measuring method even when concentration of hollow particles is low, capable of highly efficiently measuring the concentration of the hollow particles.SOLUTION: A hollow particle concentration measuring method, the method for measuring concentration of hollow particles in measuring object particles, includes: a dispersion liquid preparation step of dispersing the measuring object particles in dispersion media to acquire dispersion liquid; a sedimentation separation step of generating sediments and suspensions in the dispersion liquid; a supernatant collection step of performing operation to collect a prescribed amount in the supernatant containing floating matters to acquire measuring object liquid; a hollow particle measuring step of calculating the number of the hollow particles contained in the measuring object liquid to acquire the number of measurements; and a concentration calculation step of calculating the concentration of the hollow particles based on the number of measurements.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a method for measuring the concentration of hollow particles.

Background Art

[0002] Particulate substances such as silica particles are used, for example, as fillers for semiconductor encapsulants. By using the filler, the electrical insulation, high thermal conductivity, low thermal expansion, etc. of the semiconductor encapsulant can be improved.

[0003] In the manufacturing process of particulate substances, a small amount of hollow particles may be inadvertently mixed. If a large amount of such hollow particles are mixed, the properties of the semiconductor encapsulant will deteriorate. For this reason, a technique for detecting the concentration of hollow particles contained in the particulate substance is required.

[0004] For example, Patent Document 1 discloses observing silica particles with a transmission optical microscope, counting the number of particles in which a small circle is recognized inside the circle showing the outer shape of the particles and the number of particles in a fragmentary shape in which particles with a hollow inside are broken as the number of hollow particles, and evaluating the number of hollow particles recognized among 1000 silica particles. By such a method, the number of hollow particles among 1000 silica particles, that is, the concentration of hollow particles can be obtained.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0006] In the method described in Patent Document 1, it is necessary to observe 1000 silica particles under a microscope. Therefore, a large amount of man-hours is required, and the concentration of hollow particles cannot be easily determined. In particular, when the concentration of hollow particles is originally low, there may be no hollow particles observed among 1000 silica particles. In such a case, it is necessary to observe another 1000 silica particles again, and there is a problem that the man-hours further increase.

[0007] An object of the present invention is to provide a method for measuring the concentration of hollow particles that can efficiently measure the concentration of hollow particles even when the concentration of hollow particles is low.

Means for Solving the Problems

[0008] Such an object is achieved by the present invention of the following (1) to (8). (1) A method for measuring the concentration of hollow particles in particles to be measured, A dispersion liquid preparation step of dispersing the particles to be measured in a dispersion medium to obtain a dispersion liquid; A sedimentation separation step of generating a precipitate and a suspension in the dispersion liquid; An operation of collecting a predetermined amount in the supernatant containing the suspension to obtain a liquid to be measured, a supernatant collection step; A hollow particle measurement step of measuring the number of the hollow particles contained in the liquid to be measured to obtain a measurement number; A concentration calculation step of calculating the concentration of the hollow particles based on the measurement number; A method for measuring the concentration of hollow particles, characterized by comprising the above.

[0009] (2) The method for measuring the concentration of hollow particles according to (1) above, wherein the operation is performed in a region where the depth from the liquid surface of the dispersion liquid is shallower than 4 mm.

[0010] (3) The method for measuring the concentration of hollow particles according to (1) or (2) above, wherein the sedimentation separation step includes a centrifugation treatment on the dispersion liquid.

[0011] (4) The calculation of the concentration in the concentration calculation step is The measurement number, the amount of the particles to be measured, and the recovery rate by the operation calculated in advance, The hollow particle concentration measurement method according to any one of (1) to (3) above, which is performed based on

[0012] (5) The measurement count is When a part of the liquid to be measured is extracted and used as an observation liquid under a microscope, the number of the hollow particles contained in the observation liquid under the microscope is measured, and the obtained measurement count under the microscope is converted based on the amount of the liquid to be measured and the amount of the observation liquid under the microscope. The hollow particle concentration measurement method according to (4) above, which is a converted number.

[0013] (6) Further having a recovery rate calculation step of calculating the recovery rate in advance, In the recovery rate calculation step, when x is a positive integer starting from 1, a preliminary dispersion step of dispersing the particles to be measured as particles to be preliminarily measured in a dispersion medium to obtain an x-th dispersion liquid; a preliminary separation step of generating an x-th precipitate and an x-th floating substance in the x-th dispersion liquid; a preliminary measurement step of measuring the number of the hollow particles contained in the extract extracted from the x-th floating substance to obtain an x-th measurement count; the remaining parts other than the extract in the x-th precipitate and the x-th floating substance are used as new particles to be preliminarily measured, x is increased by 1, and the preliminary dispersion step, the preliminary separation step, and the preliminary measurement step are newly performed one or more times; a repetition step; a calculation step of calculating the recovery rate from all the obtained x-th measurement counts; The hollow particle concentration measurement method according to (4) or (5) above, which has

[0014] (7) When the x-th measurement count is f(x), The calculation of the recovery rate in the calculation step is performed by fitting processing in which a function represented by the following formula (4) is applied to a data set composed of x and the x-th measurement count obtained in the preliminary measurement step. The hollow particle concentration measurement method according to (6) above. f(x)=A(1 - R) x-1 R … (4) [In formula (4), A is the number of the hollow particles in the particles to be pre-measured. R is the ratio of the x-th measurement number to the number of the hollow particles in the particles to be pre-measured (= the recovery rate).]

[0015] (8) The method for measuring the concentration of hollow particles according to any one of (1) to (7) above, wherein the particles to be measured are silica particles.

Advantages of the Invention

[0016] According to the present invention, even when the concentration of hollow particles is low, the concentration of hollow particles can be efficiently measured.

Brief Description of the Drawings

[0017]

Figure 1

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Figure 11

Figure 12

Figure 13

Mode for Carrying Out the Invention

[0018] Hereinafter, the hollow particle concentration measurement method of the present invention will be described in detail based on the preferred embodiments shown in the accompanying drawings.

[0019] FIG. 1 is a process diagram for explaining the hollow particle concentration measurement method according to the embodiment. The hollow particle concentration measurement method according to the embodiment is a method for measuring the concentration of hollow particles 12 contained in particulate matter as the particles to be measured 10. The hollow particles 12 refer to particles with a cavity inside, and the cavity in the hollow particles 12 may not be blocked, but it is preferably blocked. In the present embodiment, the concentration of the hollow particles 12 is efficiently measured by sedimentation separation of the hollow particles 12 and other particles using the specific gravity difference. In this specification, particles other than the hollow particles 12 are also referred to as "solid particles 14".

[0020] The hollow particle concentration measurement method shown in FIG. 1 includes a dispersion liquid preparation step S102, a sedimentation separation step S104, a supernatant recovery step S106, a hollow particle measurement step S108, and a concentration calculation step S110. Hereinafter, each step will be sequentially described.

[0021] 1. Dispersion Liquid Preparation Step FIG. 2 is a diagram conceptually showing the dispersion preparation step S102 shown in FIG. 1. FIG. 3 is a diagram conceptually showing the dispersion 30 prepared in the dispersion preparation step S102 shown in FIG. 1.

[0022] In the dispersion preparation step S102, as shown in FIG. 2, the particles 10 to be measured are put into the dispersion medium 20 in the container 22 and stirred. Thereby, the particles 10 to be measured are dispersed in the dispersion medium 20, and the dispersion 30 shown in FIG. 3 is obtained.

[0023] The particles 10 to be measured include hollow particles 12 and solid particles 14. The concentration of the hollow particles 12 in the particles 10 to be measured is usually very low compared to the concentration of the solid particles 14. For example, the number concentration is less than the ppm order, that is, the ppb order or less. Therefore, when the concentration of the hollow particles 12 in the particles 10 to be measured is roughly known, it is preferable to set the amount of the particles 10 to be measured prepared in this step to an amount that probabilistically contains sufficient hollow particles 12.

[0024] The particles 10 to be measured are not particularly limited, and examples include various ceramic particles such as silica particles, alumina particles, and zirconia particles, as well as various resin particles, various metal particles, and various silicon-based substance particles.

[0025] Among these, the particles 10 to be measured are preferably silica particles. Since silica particles are chemically stable and relatively easy to obtain, they are used in various fields. Therefore, efficiently measuring the concentration of hollow particles in such silica particles is important for supplying silica particles with stable quality.

[0026] The average particle size of the particles 10 to be measured is not particularly limited, but is preferably about 0.05 to 200 μm, and more preferably about 0.1 to 50 μm.

[0027] The dispersion medium 20 is not particularly limited as long as it is a liquid having a specific gravity capable of sedimentation-separating the hollow particles 12 and the solid particles 14. Examples include water, as well as alcohols such as methanol, ethanol, and propanol.

[0028] The amount of the particles to be measured 10 added to the dispersion medium 20 is not particularly limited, as long as the particles to be measured 10 can be uniformly dispersed.

[0029] The amount of the dispersion medium 20 is not particularly limited. However, considering that it should be possible to disperse a sufficient amount of the particles to be measured 10 and that the amount should not make handling difficult, it is preferably about 5 to 1000 mL, and more preferably about 20 to 100 mL.

[0030] Stirring may be performed as necessary and may be omitted. For stirring, any mixing device, dispersing device, ultrasonic irradiation device, etc. may be used. When an ultrasonic irradiation device is used, the ultrasonic irradiation time is preferably about 1 to 300 minutes, and more preferably about 30 to 120 minutes.

[0031] Any additive may be added to the dispersion liquid 30. Examples of the additive include a dispersant such as a surfactant. The addition amount of the dispersant is not particularly limited. For example, it is about 0.1 to 10.0 g with respect to 30 mL of the dispersion liquid 30.

[0032] 2. Sedimentation separation step FIG. 4 is a diagram conceptually showing the sedimentation separation step S104 shown in FIG. 1.

[0033] In the sedimentation separation step S104, sedimentation separation is performed on the dispersion liquid 30. Sedimentation separation means that the dispersion medium 20 is selected so that the specific gravity of the hollow particles 12 contained in the particles to be measured 10 is smaller than the specific gravity of the dispersion medium 20, and the specific gravity of the solid particles 14 is larger than the specific gravity of the dispersion medium 20, thereby generating a sediment 32 and a suspension 34 in the dispersion liquid 30. Immediately after the dispersion liquid preparation step S102, the particles to be measured 10 are uniformly dispersed in the dispersion liquid 30. However, as time passes, due to the specific gravity difference, particles that settle to the bottom of the container 22 and particles that float near the liquid surface of the dispersion liquid 30 are generated. Thereby, the sediment 32 and the suspension 34 shown in FIG. 4 are obtained. The sediment 32 contains a large amount of solid particles 14, but may also contain hollow particles 12. The suspension 34 contains a large amount of hollow particles 12, but may also contain solid particles 14.

[0034] In the sedimentation separation step S104, the dispersion liquid 30 may be left standing until the sedimentation separation is completed. However, if necessary, a treatment for promoting separation such as centrifugation that applies a centrifugal acceleration may be used in combination. For example, when performing the centrifugation treatment, a centrifugal acceleration may be applied toward the bottom of the container 22. Thereby, the sedimentation separation is promoted, and the sediment 32 and the suspension 34 can be obtained in a shorter time. The number of rotations applied to the container 22 in the centrifugation treatment varies depending on the distance from the rotation axis to the container 22 and the like, but as an example, it is preferably 2000 to 10000 rpm. Also, the time for performing the centrifugation treatment is appropriately set according to the number of rotations and the amount of the particles to be measured 10 introduced into the dispersion liquid 30, but as an example, it is preferably 5 to 120 minutes.

[0035] 3. Supernatant recovery step In the supernatant recovery step S106, an operation is performed to recover a predetermined amount of the supernatant in the dispersion liquid 30. Hereinafter, this operation is referred to as the "supernatant recovery operation". As a result, the liquid to be measured 40 shown in FIG. 4 is obtained. The supernatant refers to the portion near the liquid surface of the dispersion liquid 30. For the supernatant recovery operation, for example, a pipette or the like is used. The predetermined amount is appropriately set according to the size of the opening of the container 22 and the like. As an example, it is preferably about 3 to 40% of the amount of the dispersion medium 20, and more preferably about 5 to 15%. If it is within this range, the working efficiency can be improved. Also, as a specific predetermined amount, for example, it is about 1 to 50 mL.

[0036] Also, the supernatant recovery operation may be performed multiple times. Specifically, for example, when performing the supernatant recovery operation using a suction tool such as a pipette, the operation of sucking the supernatant with the pipette may be performed multiple times, and the suction liquids for multiple times may be combined as the liquid to be measured 40. In this case, it is preferable to set the position of the tip of the pipette at the same position in the horizontal and vertical directions in multiple operations. Thereby, the calculation accuracy of the concentration can be improved.

[0037] In order to improve the reproducibility of the position of the tip of the pipette in the horizontal and vertical directions, the relative position of the pipette with respect to the container 22 may be measured, for example, with a laser displacement meter or the like.

[0038] Note that the position of the tip of the pipette in the supernatant recovery operation may affect the number of hollow particles 12 contained in the liquid to be measured 40. Therefore, it is preferable to optimize the position of the tip of the pipette as follows in the horizontal and vertical directions. Thereby, the number of hollow particles 12 contained in the liquid to be measured 40 can be increased, and the calculation accuracy of the concentration can be improved.

[0039] FIG. 5 is a plan view of the container 22 containing the dispersion liquid 30 as viewed from vertically above. FIG. 5 illustrates an example in which the plan view shape of the container 22 is a circle with a radius r. In FIG. 5, the range of the container 22 viewed in plan is divided into three concentric regions. In FIG. 5, these three regions are referred to as a central portion 224, an intermediate portion 226, and an edge portion 228. The central portion 224 is a circular region with a radius of 0.2r from the center O of the range of the container 22 viewed in plan. The intermediate portion 226 is adjacent to the outside of the central portion 224 and is an annular region with a difference between the inner radius and the outer radius of 0.6r. The edge portion 228 is adjacent to the outside of the intermediate portion 226 and is an annular region with a difference between the inner radius and the outer radius of 0.2r.

[0040] In the supernatant recovery operation, it is preferable to place the tip of the pipette in the horizontal direction at the edge portion 228. Thereby, the probability of recovering more hollow particles 12 can be increased compared to the case where the tip of the pipette is placed in the central portion 224 or the intermediate portion 226.

[0041] FIG. 6 is a graph showing the relationship between the position of the tip of the pipette in the horizontal direction and the number of hollow particles 12 that can be recovered when a supernatant recovery operation is performed on the suspension 34 containing a predetermined amount of hollow particles 12. In FIG. 6, the number of hollow particles 12 that can be recovered by performing the supernatant recovery operation three times is plotted for each position of the tip of the pipette in the horizontal direction. As shown in FIG. 6, it is confirmed that more hollow particles 12 can be recovered at the edge portion 228 compared to the central portion 224 and the intermediate portion 226.

[0042] FIG. 7 is a cross-sectional view of the container 22 containing the dispersion liquid 30 cut along a vertical plane perpendicular to the horizontal plane. In FIG. 7, a region where the depth d from the liquid surface 302 of the dispersion liquid 30 is shallower than 4 mm is defined as a surface layer portion 334.

[0043] In the supernatant recovery operation, it is preferable to place the tip of the pipette P in the vertical direction at the surface layer portion 334. Thereby, the probability of recovering more hollow particles 12 can be increased compared to the case where the tip of the pipette is deeper than the surface layer portion 334.

[0044] In addition, the position of the tip of the pipette P is preferably placed in the surface layer portion 334, particularly in a region shallower than 3 mm from the liquid surface 302, and more preferably in a range shallower than 2 mm.

[0045] FIG. 8 is a graph showing the relationship between the position of the tip of the pipette in the vertical direction and the number of hollow particles 12 that could be recovered when a supernatant recovery operation was performed on the suspension 34 containing a predetermined amount of hollow particles 12. In FIG. 8, the number of hollow particles 12 that could be recovered after performing the supernatant recovery operation three times is plotted for each position of the tip of the pipette in the vertical direction. As shown in FIG. 8, it is confirmed that the hollow particles 12 can be recovered if the position of the tip of the pipette is within 3 mm in depth from the liquid surface 302, and in particular, if it is within 1 mm in depth, many hollow particles 12 can be recovered. Although not shown in FIG. 8, when the position of the tip of the pipette is more than 4 mm in depth from the liquid surface 302, the number of hollow particles 12 that could be recovered is less than the number shown in FIG. 8.

[0046] 4. Hollow Particle Measurement Step FIGS. 9 and 10 are diagrams conceptually showing the hollow particle measurement step S108 shown in FIG. 1.

[0047] In the hollow particle measurement step S108, the number of hollow particles 12 contained in the liquid to be measured 40 is measured to obtain the measurement number n 40 and obtain.

[0048] Here, let the amount of the particles to be measured 10 put into the dispersion medium 20 in the dispersion liquid preparation step S102 described above be w 10 and. Also, a certain reproducibility is recognized in the ratio of the number of hollow particles 12 that transfer to the liquid to be measured 40 among the hollow particles 12 contained in the particles to be measured 10. Therefore, using this reproducibility, this ratio is obtained in advance as the recovery rate R. The method for obtaining the recovery rate R will be described later.

[0049] Then, in the concentration calculation step S110 described later, the measurement number n 40 , the amount w of the particles to be measured 10 10Based on the recovery rate R and the like, the concentration c of the hollow particles 12 in the particles 10 to be measured can be obtained from the following formula (1). 12 It can be determined.

[0050] [Number]

[0051] If this measurement number n 40 is directly sought, it is necessary to measure all the hollow particles 12 contained in the liquid 40 to be measured. Then, depending on the amount of the liquid 40 to be measured, a large amount of man-hours may be required. Therefore, in the present embodiment, after measuring the number of the hollow particles 12 contained in a part of the liquid 40 to be measured, the measurement number n 40 is obtained by conversion. The method will be described below.

[0052] First, as shown in FIG. 9, a part of the liquid 40 to be measured is extracted to obtain a liquid 50 for microscopic observation. The liquid 50 for microscopic observation refers to a sample to be magnified and observed by a microscope or the like described later. The amount of the liquid 50 for microscopic observation is appropriately set according to the concentration of the hollow particles 12 in the particles 10 to be measured, the width of the field of view of the microscope, etc. As an example, it is preferably about 0.01 to 10% of the amount of the liquid 40 to be measured, and more preferably about 0.10 to 1.0%. Thereby, the probability that a sufficient number of hollow particles 12 are contained in the liquid 50 for microscopic observation is increased, and it is possible to prevent the number of the hollow particles 12 to be measured under the microscope from becoming excessively large. Therefore, while improving the calculation accuracy of the concentration, the efficiency of this step can be improved. The specific amount of the liquid 50 for microscopic observation is, for example, about 1 to 100 μL.

[0053] Next, as shown in FIG. 10, the liquid 50 for microscopic observation is observed with a microscope 52. The microscope 52 may be a magnifying glass, a digital microscope, or the like in addition to an optical microscope. Then, the number of the hollow particles 12 contained in the liquid 50 for microscopic observation is measured to obtain a microscopic measurement number n 50 .

[0054] Next, based on the obtained microscopic measurement count n 50 , the amount V of the liquid 40 to be measured 40 , and the amount V of the microscopic observation liquid 50 50 , the measurement count n 40 is calculated from the following formula (2).

[0055]

Equation

[0056] In the above manner, the microscopic measurement count n 50 can be converted to the measurement count n 40 . According to such a method, the number of hollow particles 12 contained in the microscopic observation liquid 50, which is less than the total number of hollow particles 12 contained in the liquid 40 to be measured, that is, the microscopic measurement count n 50 is obtained, and thus the measurement count n 40 can be calculated. Therefore, the man-hour of the hollow particle measurement step S108 can be reduced.

[0057] 5. Concentration calculation step In the concentration calculation step S110, based on the measurement count n 40 , the concentration c 12 of the hollow particles 12 in the particles 10 to be measured is calculated. The above formula (1) can be used for this calculation.

[0058] When the above formula (2) is substituted into the above formula (1), the following formula (3) is derived.

[0059]

Equation

[0060] When the above formula (3) is used, apparently, the concentration c 40 of the hollow particles 12 in the particles 10 to be measured can be calculated without obtaining the measurement count n 12 . However, as described above, since the above formula (2) is included in the above formula (3), based on the above formula (3), the concentration c 12Even when calculating, it invariably goes through the process of calculating the number of measurements n 40 It must have gone through the process of calculating it.

[0061] As described above, the method for measuring the concentration of hollow particles according to the present embodiment measures the concentration c of the hollow particles 12 in the particles 10 to be measured 12 It is a method, and includes a dispersion liquid preparation step S102, a sedimentation separation step S104, a supernatant recovery step S106, a hollow particle measurement step S108, and a concentration calculation step S110. In the dispersion liquid preparation step S102, the particles 10 to be measured are dispersed in the dispersion medium 20 to obtain a dispersion liquid 30. In the sedimentation separation step S104, a sediment 32 and a suspension 34 are generated in the dispersion liquid 30. In the supernatant recovery step S106, an operation of recovering a predetermined amount in the supernatant containing the suspension 34 is performed to obtain the liquid 40 to be measured. In the hollow particle measurement step S108, the number of hollow particles 12 contained in the liquid 40 to be measured is measured, and the number of measurements n 40 is obtained. In the concentration calculation step S110, based on the number of measurements n 40 , the concentration c of the hollow particles 12 12 is calculated.

[0062] According to such a configuration, since it has the sedimentation separation step S104, even when the concentration c of the hollow particles 12 in the particles 10 to be measured is low, the liquid 40 to be measured in which the hollow particles 12 are concentrated can be obtained. Then, after measuring the number of hollow particles 12 contained in the liquid 40 to be measured, the concentration c of the hollow particles 12 is calculated from the obtained number of measurements n 12 , so the man-hours required for measurement can be reduced. Therefore, even when the concentration c of the hollow particles 12 is low, the concentration c of the hollow particles 12 40 can be efficiently measured. 12 12 12

[0063] Also, the above-described supernatant recovery operation is preferably performed in a region where the depth from the liquid surface 302 of the dispersion liquid 30 is shallower than 4 mm, that is, the surface layer portion 334. Thereby, the probability of recovering more hollow particles 12 is increased, so the concentration c of the hollow particles 12 12In the calculation, the calculation accuracy can be improved. In addition, since the man-hours required to collect the necessary number of hollow particles 12 can be reduced, the measurement efficiency can be enhanced.

[0064] Further, the sedimentation separation step S104 preferably includes a centrifugation process for the dispersion liquid 30. Thereby, sedimentation separation is promoted, and the sediment 32 and the floating matter 34 can be obtained in a short time. Also, the separability in sedimentation separation can be enhanced.

[0065] Also, the concentration c of the hollow particles 12 in the concentration calculation step S110 12 is preferably calculated based on the measurement count n 40 , the amount w of the particles to be measured 10 10 , and the recovery rate R obtained by a supernatant recovery operation calculated in advance.

[0066] According to such a calculation method, from the number of hollow particles 12 contained in the concentrated liquid to be measured 40, using the recovery rate R, the concentration c of the hollow particles 12 12 can be efficiently calculated.

[0067] Also, in the present embodiment, as described above, a part of the liquid to be measured 40 is extracted to obtain the microscopic observation liquid 50. Then, the measurement count n 40 is preferably the number obtained by measuring the number of hollow particles 12 contained in the microscopic observation liquid 50 and converting the obtained microscopic measurement count n 50 based on the amount V of the liquid to be measured 40 40 and the amount V of the microscopic observation liquid 50. 50 Based on such a calculation method, the number of hollow particles 12 contained in the microscopic observation liquid 50, which is less than the total number of hollow particles 12 contained in the liquid to be measured 40, that is, the microscopic measurement count n

[0068] is obtained, and the measurement count n 50 can be calculated. Therefore, the man-hours of the hollow particle measurement step S108 can be reduced. 40

[0069] 6. Recovery rate calculation step The above formula (1) includes the recovery rate R. This recovery rate R is an index representing the ratio of the measurement number n to the number of hollow particles 12 in the measured particles 10. However, this index tends to fall within a certain value in the above-described supernatant recovery operation as long as the conditions such as the measured particles 10 and the dispersion medium 20 do not change. Utilizing this, by calculating the recovery rate R in advance, the measurement efficiency of the concentration c of the hollow particles 12 40 can be increased. Therefore, prior to the calculation of the concentration c 12 , it is preferable to have a step (recovery rate calculation step S202) of calculating the recovery rate R in advance using the measured particles 10 to be measured and the dispersion medium 20 used for the measurement, etc. 12

[0070] FIG. 11 is a process diagram for explaining the recovery rate calculation step S202 included in the hollow particle concentration measurement method according to the embodiment.

[0071] The recovery rate calculation step S202 shown in FIG. 11 includes a preliminary dispersion step S204, a preliminary separation step S206, a preliminary measurement step S208, a determination step S210, a repetition step S212, and a calculation step S214. Hereinafter, each step will be sequentially described.

[0072] 6.1. Preliminary dispersion step In the preliminary dispersion step S204, a first x dispersion liquid similar to the above-described dispersion liquid 30 is prepared in advance. x is a positive integer starting from 1. Therefore, in the first preliminary dispersion step S204, a first dispersion liquid is prepared. The first dispersion liquid is prepared by dispersing the above-described measured particles 10 as particles to be preliminarily measured in a dispersion medium similar to the dispersion medium 20.

[0073] When preparing the first dispersion liquid, the input amount of the particles to be preliminarily measured may be different from the input amount of the measured particles 10 when adjusting the dispersion liquid 30 in the above-described dispersion liquid preparation step S102, but it is preferably the same. Thereby, a highly accurate recovery rate R can be calculated.

[0074] ​Also, regarding conditions such as stirring and the type and amount of additives added, etc., they may be different from those in the dispersion preparation step S102 described above, but it is preferable that they be the same as those in the dispersion preparation step S102 described above.

[0075] 6.2. Preliminary separation step In the first preliminary separation step S206, sedimentation separation is performed on the first dispersion liquid. As a result, a first sediment and a first floating substance are generated in the first dispersion liquid.

[0076] The conditions for sedimentation separation, the presence or absence and conditions of centrifugation treatment, etc. may be different from those in the sedimentation separation step S104 described above, but it is preferable that they be the same. Thereby, a high-precision recovery rate R can be calculated.

[0077] 6.3. Preliminary measurement step In the first preliminary measurement step S208, the number of hollow particles 12 contained in a predetermined amount of the extract extracted from the first floating substance is measured to obtain a first measurement number. This predetermined amount may be different from the predetermined amount in the supernatant recovery step S106 described above, but it is preferably the same. When obtaining the first measurement number, similar to the calculation of the measurement number n 40 in the hollow particle measurement step S108 described above, the total number of hollow particles 12 contained in the extract may be measured, or a part of the extract may be extracted to be used as a microscopic observation liquid, and it may be converted from the number of hollow particles 12 (microscopic measurement number) contained therein.

[0078] 6.4. Judgment step In the determination step S210, it is determined whether to end the measurements necessary for calculating the recovery rate R. If the data necessary for calculating the recovery rate R has been acquired, the measurements are ended and the operation step S214 is entered. If the data necessary for calculating the recovery rate R has not been acquired, the iterative step S212 is entered. Although details will be described later, in the iterative step S212, the first precipitate generated in the first preliminary separation step S206 and the remainder that could not be extracted from the first floating matter are used as new particles to be preliminarily measured, and the second or subsequent preliminary dispersion step S204, preliminary separation step S206, and preliminary measurement step S208 are performed. Thereby, more data necessary for calculating the recovery rate R can be acquired, and the accuracy of the recovery rate R is improved. Therefore, in the determination step S210, it is preferably determined to perform at least one iterative step S212.

[0079] 6.5. Iterative Step As described above, the iterative step S212 performs the preliminary dispersion step S204, preliminary separation step S206, and preliminary measurement step S208 one or more times. As a result, in the entire recovery rate calculation step S202, these steps are repeated two or more times.

[0080] In the iterative step S212, as described above, the first precipitate generated in the first preliminary separation step S206 and the remainder other than the extract in the first floating matter are used as new particles to be preliminarily measured. In the following description, the remainder other than the extract in the x-th floating matter is abbreviated as "the remainder of the x-th floating matter". Then, x is incremented by one, and in the second preliminary dispersion step S204, the second dispersion liquid is prepared. In the second preliminary separation step S206, a second precipitate and a second floating matter are generated in the second dispersion liquid. In the second preliminary measurement step S208, a second measurement number is obtained.

[0081] Thereafter, when continuing the iterative step S212, x is incremented by one again, and the third preliminary dispersion step S204, third preliminary separation step S206, and third preliminary measurement step S208 are performed to obtain a third measurement number.

[0082] FIG. 12 is a conceptual diagram for explaining the model used to calculate the recovery rate R in the recovery rate calculation step S202 shown in FIG. 11. The "number of executions" in FIG. 12 is the number of times the preliminary dispersion step S204, the preliminary separation step S206, and the preliminary measurement step S208 are executed. Also, "A" in FIG. 12 is the number of hollow particles 12 in the particles to be preliminarily measured.

[0083] In the first execution, from the particles to be preliminarily measured containing the hollow particles 12 with the number A, through the first preliminary dispersion step S204, the first preliminary separation step S206, and the first preliminary measurement step S208, the above-mentioned first measurement number is obtained. The recovery rate R is an index representing the ratio of the measurement number n40 to the number of hollow particles 12 in the particles to be measured 10 in the above-mentioned hollow particle measurement step S108. Therefore, the recovery rate R can be regarded as the ratio of the first measurement number to the number A. Thus, the first measurement number can be expressed as the product AR of the number A and the recovery rate R.

[0084] On the other hand, the number of hollow particles 12 contained in the portion combining the first sediment and the remainder of the first floating matter can be expressed as the product A(1 - R) of the number A and the non-recovery rate (1 - R). Then, the number of hollow particles 12 contained in the new particles to be preliminarily measured subjected to the second preliminary dispersion step S204 can be expressed as A(1 - R).

[0085] In the second execution, from the new particles to be preliminarily measured containing the hollow particles 12 with the number A(1 - R), through the second preliminary dispersion step S204, the second preliminary separation step S206, and the second preliminary measurement step S208, the above-mentioned second measurement number is obtained. The recovery rate R can be regarded as the ratio of the second measurement number to the number A(1 - R). Therefore, the second measurement number can be expressed as the product A(1 - R)R of the number A(1 - R) and the recovery rate R.

[0086] On the other hand, the number of hollow particles 12 contained in the portion combining the second sediment and the remainder of the second floating matter can be expressed as the product A(1 - R) of the number A(1 - R) and the non-recovery rate (1 - R). 2 Then, the number of hollow particles 12 contained in the new particles to be preliminarily measured subjected to the third preliminary dispersion step S204 can be expressed as A(1 - R). 2can be expressed as

[0087] In the third execution, from the new particles to be pre-measured containing the hollow particles 12 of A(1 - R), through the third pre-dispersion step S204, the third pre-separation step S206, and the third pre-measurement step S208, the above-mentioned third measurement count is obtained. The recovery rate R can be regarded as the ratio of the third measurement count to A(1 - R). Therefore, the third measurement count is the product A(1 - R) 2 and R, which can be expressed as A(1 - R) 2 R 2 and the recovery rate R, which is the product A(1 - R) 2 R and can be expressed as

[0088] On the other hand, the number of hollow particles 12 contained in the part combining the third sediment and the remainder of the third floating matter is the product of A(1 - R) 2 and the non-recovery rate (1 - R), which can be expressed as A(1 - R) 3 Then, the number of hollow particles 12 contained in the new particles to be pre-measured subjected to the fourth pre-dispersion step S204 can be expressed as A(1 - R) 3 and can be expressed as

[0089] Based on the above, in the x-th pre-dispersion step S204 of the execution times, the x-th dispersion liquid is prepared. In the x-th pre-separation step S206, the x-th sediment and the x-th floating matter are generated. In the x-th pre-measurement step S208, the x-th measurement count is obtained. On the other hand, this x-th measurement count is theoretically represented by the function f(x)=A(1 - R) x-1 R

[0090] Then, for the data set composed of the execution times x and the x-th measurement count obtained in the pre-measurement step S208, if fitting processing is performed to fit this function, the number A and the recovery rate R closest to the model shown in FIG. 12 can be obtained from the x sets of data.

[0091] FIG. 13 is a graph showing the results of trying the recovery rate calculation step for samples with n = 1, n = 2, and n = 3, where the horizontal axis is the number of executions x and the vertical axis is the x-th measurement number. The three samples are pre-measured particles extracted from the same sample. FIG. 13 also shows the number A and the recovery rate R obtained by fitting the above function to each test result, as well as an approximate curve representing the result of the fitting process.

[0092] As shown in FIG. 13, when the recovery rate R is calculated independently from the three samples, the recovery rate R is within a relatively narrow range. From this, it can be said that according to the above-described recovery rate calculation step, a highly reproducible and highly accurate recovery rate R can be obtained.

[0093] As described above, the hollow particle concentration measurement method according to the embodiment further includes a recovery rate calculation step S202 for calculating the recovery rate R in advance. When x is a positive integer starting from 1, this recovery rate calculation step S202 includes a preliminary dispersion step S204, a preliminary separation step S206, a preliminary measurement step S208, a repetition step S212, and a calculation step S214. The preliminary dispersion step S204 disperses the particles to be measured 10 as pre-measured particles in a dispersion medium to obtain an x-th dispersion liquid. In the preliminary separation step S206, an x-th precipitate and an x-th suspension are generated in the x-th dispersion liquid. In the preliminary measurement step S208, the number of hollow particles 12 contained in the extract extracted from the x-th suspension is measured to obtain the x-th measurement number. In the repetition step S212, the remainder other than the extract in the x-th precipitate and the x-th suspension is used as new pre-measured particles, x is incremented by 1, and the preliminary dispersion step S204, the preliminary separation step S206, and the preliminary measurement step S208 are newly performed one or more times. In the calculation step S214, the recovery rate R is calculated from all the obtained x-th measurement numbers.

[0094] According to such a configuration, a highly accurate recovery rate R can be efficiently calculated. By using the calculated recovery rate R, in the above-described concentration calculation step S110, the concentration c of the hollow particles 12 in the particles to be measured 10 12 can be accurately and efficiently calculated.

[0095] Also, as described above, when the x-th measurement number is f(x), the calculation of the recovery rate R in the calculation step S214 is performed by fitting processing in which a function represented by the following formula (4) is applied to a data set composed of the number of executions x and the x-th measurement number obtained in the preliminary measurement step S208. f(x)=A(1 - R) x-1 R … (4) [In formula (4), A is the number of hollow particles 12 in the particles to be preliminarily measured. R is the ratio of the x-th measurement number to the number of hollow particles 12 in the particles to be preliminarily measured (= recovery rate R).]

[0096] By using such a method, it is possible to efficiently calculate the recovery rate R with particularly high accuracy.

[0097] The method for measuring the concentration of hollow particles of the present invention has been described based on the illustrated embodiments, but the present invention is not limited thereto.

[0098] For example, in the method for measuring the concentration of hollow particles of the present invention, steps for any purpose may be added to the above-described embodiments.

Explanation of Signs

[0099] 10 Particles to be measured 12 Hollow particles 14 Solid particles 20 Dispersion medium 22 Container 30 Dispersion 32 Sediment 34 Suspension 40 Liquid to be measured 50 Liquid for microscopic observation 52 Microscope 224 Central part 226 Intermediate part 228 Edge part 302 Liquid surface 334 Surface layer part O Center P Pipette S102 Dispersion Preparation Process S104 Sedimentation Separation Process S106 Supernatant Recovery Process S108 Hollow Particle Measurement Process S110 Concentration Calculation Process S202 Recovery Rate Calculation Process S204 Preliminary Dispersion Process S206 Preliminary Separation Process S208 Preliminary Measurement Process S210 Judgment Process S212 Repetition Process S214 Calculation Process d Depth r Radius

Claims

1. A method for measuring the concentration of hollow particles in a particle to be measured, comprising: a dispersion preparation step of dispersing the particle to be measured in a dispersion medium to obtain a dispersion; a sedimentation separation step of generating a sediment and a suspension in the dispersion; a supernatant recovery step of performing an operation of recovering a predetermined amount in the supernatant containing the suspension to obtain a liquid to be measured; a hollow particle measurement step of measuring the number of the hollow particles contained in the liquid to be measured to obtain a measured number; a concentration calculation step of calculating the concentration of the hollow particles based on the measured number; A method for measuring the concentration of hollow particles, characterized by comprising the above steps.

2. The method for measuring the concentration of hollow particles according to claim 1, wherein the operation is performed in a region where the depth from the liquid surface of the dispersion is shallower than 4 mm.

3. The method for measuring the concentration of hollow particles according to claim 1 or 2, wherein the sedimentation separation step includes a centrifugation treatment on the dispersion.

4. The calculation of the concentration in the concentration calculation step is based on the measured number, the amount of the particle to be measured, and the recovery rate calculated in advance by the operation, The method for measuring the concentration of hollow particles according to any one of claims 1 to 3.

5. The measured number is when a part of the liquid to be measured is extracted to obtain an observation liquid under a microscope, the number of the hollow particles contained in the observation liquid under the microscope is measured, and the obtained measured number under the microscope is converted based on the amount of the liquid to be measured and the amount of the observation liquid under the microscope. The method for measuring the concentration of hollow particles according to claim 4.

6. further comprising a recovery rate calculation step of calculating the recovery rate in advance, wherein in the recovery rate calculation step, when x is a positive integer starting from 1, a preliminary dispersion step of dispersing the particle to be measured as a particle to be preliminarily measured in a dispersion medium to obtain an x-th dispersion; a preliminary separation step of generating an x-th sediment and an x-th suspension in the x-th dispersion; a preliminary measurement step of measuring the number of the hollow particles contained in an extract extracted from the x-th suspension to obtain an x-th measured number; a repetition step of using the remaining parts other than the extract in the x-th sediment and the x-th suspension as new particles to be preliminarily measured, increasing the x by 1, and newly performing the preliminary dispersion step, the preliminary separation step, and the preliminary measurement step one or more times; a calculation step of calculating the recovery rate from all the obtained x-th measured numbers; The method for measuring the concentration of hollow particles according to claim 4 or 5, characterized by comprising the above steps.

7. When the x-th measured number is f(x), The method for measuring the hollow particle concentration according to claim 6, wherein the calculation of the recovery rate in the arithmetic process is performed by fitting processing in which a function represented by the following formula (4) is applied to a data set composed of the x and the x-th measurement number obtained in the preliminary measurement process. f(x) = A(1 - R) ｘ－１ R … (4) [In formula (4), A is the number of the hollow particles in the particles to be preliminarily measured. R is the ratio of the x-th measurement number to the number of the hollow particles in the particles to be preliminarily measured (= the recovery rate).]

8. The method for measuring the hollow particle concentration according to any one of claims 1 to 7, wherein the particles to be measured are silica particles.

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