CN113405954B - Method for determining wide-distribution solid granularity standard substance of dry dispersion system applied to laser diffraction granularity analyzer - Google Patents
Method for determining wide-distribution solid granularity standard substance of dry dispersion system applied to laser diffraction granularity analyzer Download PDFInfo
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Abstract
The invention provides a method for determining the particle size of a wide-distribution solid particle size standard substance of a dry dispersion system applied to a laser diffraction particle size analyzer, which is particularly used for determining the particle size of the wide-distribution solid particle size standard substance with the particle size of 1-20 mu m aiming at the dry dispersion system of the laser diffraction particle size analysis; the method can control the relative uncertainty generated in the process of the fixed value to be at a lower level so as to meet the national standard requirement.
Description
Technical Field
The invention relates to a method for determining the value of a wide-distribution solid granularity standard substance applied to a dry dispersion system of a laser diffraction granularity analyzer, and belongs to the technical field of chemical analysis.
Background
The measurement requirements of particle size are widely found in the fields of energy, chemical industry, food, pharmaceutical industry and the like. Particle size measurement instruments, such as particle sizers, have become an important tool for characterization of the particle size and distribution of micrometer-nanometer particles. And the accuracy of the measuring instrument requires the calibration and verification of the particle size standard substance. The particle size standard substance is an effective carrier for particle size measurement and also determines the accuracy and reliability of particle size measurement to a great extent.
Laser diffraction particle size analysis, which has been becoming the mainstay of particle size analysis for the 21 st century, has been becoming more mature through decades of development and application from the beginning of its creation. The market share of the laser diffraction particle sizer in China is up to 60-70%; the advantages are mainly that: mature advanced measurement principle; the measuring range is wide, about 20 nanometers to 2000 micrometers, and the particle size range of multiple orders of nanometers, submicron and microns is covered; the measurement speed is high, the test time is irrelevant to the particle size distribution of the sample, and the typical test process is generally less than one minute; scanning the sample for multiple times for each test, and the test result has good repeatability; the sample injection mode is various, and can be suitable for various types of samples.
The laser diffraction particle size analysis has high requirements on the particle size standard substance. The standard substances for instrument performance verification are also required in ISO 13320:2009 "particle size analysis-laser diffraction method": "particles of standard substance should be spherical, have suitable density and optical properties, and be suitable for use in laser diffraction techniques, particle size distribution D 90 And D 10 The ratio of (2) should be 1.5 to 10."
In general, the particle size measuring instrument is calibrated by mainly adopting a standard particle sample with narrow distribution, and the particle size distribution is relatively concentrated and can be approximately regarded as a particle sample with single particle size. For particles with narrow distribution or monodispersity, the particle size analysis result of the laser diffraction method shows that the particle size has a certain distribution range, and the measurement result of the laser diffraction method has a certain error in the analysis of the particle size distribution, namely the particles with narrow distribution or monodispersity are not suitable for the particle size analysis of the laser diffraction method, which is different from the prior identification. However, with the improvement of the particle size measurement standard, the current particle size standard substance, especially the standard substance suitable for the particle size analysis by the laser diffraction method, is turned to the wide-distribution particle size standard substance in a plurality of ways.
The national quality supervision bureau issued JJF1211-2008 "laser particle sizer calibration standard" in 2008, and clearly defined the particle size of the standard substance for instrument calibration and the uncertainty of the standard value thereof, see table 1 below.
TABLE 1
| D 50 Magnitude range | Uncertainty of standard substance |
| 1μm<D 50 <5μm | 5％，k＝2 |
| 5μm<D 50 <20μm | 3％，k＝2 |
| 20μm<D 50 <100μm | 2.5％，k＝2 |
| D 50 >100μm | 2.5％，k＝2 |
For 20 μm<D 50 <100 μm and D 50 >100 μm particles, the uncertainty of the standard substance is relatively easy to control at a low level.
But smaller than 20 μm, e.g. 1 μm<D 50 <5 μm and 5 μm<D 50 <Particles of 20 μm, the relative uncertainty of the standard substance is difficult to control; in particular, the wide-distribution solid particle size standard substances currently used in dry dispersions for laser diffraction particle size analysis generally have a relative uncertainty of 5.7% or more, exceeding the values of 3% and 5% required in table 1.
Therefore, those skilled in the art desire to improve the existing method for determining the value of the wide-distribution solid particle size standard substance, control the relative uncertainty of the standard substance, and develop the wide-distribution solid particle size standard substance which is suitable for a dry dispersion system of laser diffraction particle size analysis and meets the requirements of the national specifications.
Disclosure of Invention
In order to solve the technical problems, the invention provides a method for determining the value of a wide-distribution solid granularity standard substance of a dry dispersion system applied to a laser diffraction granularity analyzer, wherein,
the constant value method comprises the following steps in sequence:
step 1): initial samples were selected: the initial sample is selected as glass microsphere particles, the sphericity of the particles is more than 95%, the range of the expected characteristic particle diameter D50 is 1-20 microns, and the range of the ratio of the expected characteristic particle diameter D90 to the D10 is 1.5-10;
step 2): preparation of particle samples: dispersing the initial sample to prepare a particle sample in a state that single particles are independent and uniformly dispersed;
step 3): estimating: obtaining the estimated particle size distribution data of the particle sample prepared in the step 2);
the estimated particle size distribution data is obtained by artificial assumption or experimental means;
the estimated particle size distribution data comprises an estimated characteristic particle size D50, an estimated particle size distribution range and a corresponding particle size standard deviation;
step 4): simulating and calculating a representative minimum particle statistics value required for obtaining a fixed value;
the simulation calculation comprises the following steps:
step a): performing Gaussian fitting on the estimated particle size distribution data to obtain a corresponding volume distribution curve;
step b): setting the total volume of the particle sample prepared in the step 2) as V, and dividing the volume distribution curve into equal n parts of subintervals; in each subinterval i (i= … n), the particle size values in the interval are repeatedly and randomly generated until the sum of the volumes corresponding to the particle size values in the interval reaches the theoretical volume V occupied by the particle size interval i At this time, the number of particle diameter values in each sub-interval is N i ；
Step c): combining the particle size values of each subinterval to form a simulation sampling pool with the number of N, randomly taking L particle size values from the simulation sampling pool, and carrying out statistical analysis on the L particle size values to obtain a corresponding simulation statistical characteristic particle size D50;
step d): comparing the simulated statistical particle size D50 obtained in step c) with the estimated characteristic particle size D50 and calculating an error; when the fluctuation range of the error value is +/-0.3-0.4%, the corresponding minimum L value is the minimum particle statistics value;
step 5) scanning imaging, statistics and analysis:
scanning and imaging the particle sample prepared in the step 2) by using a scanning electron microscope;
and (3) measuring the diameters of the particles imaged by scanning one by adopting an internal standard method, and carrying out statistical analysis according to the minimum particle statistics value obtained in the step (4) to obtain the actual particle size distribution and particle characteristic particle size D50 and the measurement uncertainty corresponding to the particle characteristic particle size D50.
Preferably, the particle sample preparation of step 2) includes a rotary cross-dividing operation and a high pressure dispersing operation;
the operation of the rotary cross-division is as follows: adopting a dry powder disperser to carry out rotary cross shrinkage on the initial sample selected in the step 1), wherein the mass of the obtained separated sample is 0.01 g-0.05 g;
the operation of the high pressure dispersion is as follows: and placing the separated samples in a sample groove arranged at the upper part of the closed space, dispersing the particles of the separated samples into a plurality of round holes uniformly distributed around the sample groove in a high-pressure spraying mode, and freely settling the round holes on a sample table below to obtain the particle samples in a single-particle independent and uniform dispersion state.
Preferably, the initial product selected in the step 1) is shrunk to 10 g/bottle step by adopting rotary cross shrinkage, after the uniformity test among bottles, the relative uncertainty contributed by the non-uniformity among the bottles of the particle characteristic particle diameter D50 value among each bottle is controlled, 1 bottle is randomly selected, and rotary cross shrinkage is continued to 0.01 g-0.05 g.
Preferably, the ratio of the diameter of the sample groove, the diameter of the plane formed by the plurality of round holes and the diameter of the plane on which the particle sample is distributed on the sample table is 1:2: 6-1: 3:9, a step of performing the process;
the ratio of the planar diameter of the particle sample distribution on the sample table to the height of the closed space is 1:1 to 1:2.
preferably, the diameter of the round hole is 1-5 mm.
Preferably, in said step 1), the expected characteristic particle diameter D50 of the sample is selected to be in the range of 8-12 microns;
in the step 3), the diameter of the round hole is 2-4 mm; the diameter of the sample groove is 0.8-1.2 cm; the number of the round holes is 11-13;
the injection pressure of the high-pressure injection is 3-5 bar;
the vertical height from the round hole to the sample table is 11-13 cm; the diameter range of the plane of the particle sample distribution on the sample table is 7-9 cm;
in the step 5), the magnification of the scanning electron microscope is 5000 times, and the imaging resolution is 1534×1024.
Preferably, the estimated particle size distribution data is obtained by experimental means; the experimental means is that the estimated particle size distribution data is obtained by rough measurement by a laser diffraction particle size analyzer, or the estimated particle size distribution data is obtained by randomly acquiring a particle image by a scanning electron microscope and performing image processing.
Preferably, in the step 5), when the estimated characteristic particle diameter D50 is 1 to 5 μm, the magnification of the scanning electron microscope is set to 20000 times, and the imaging resolution is set to 1536×1024;
when the estimated characteristic particle diameter D50 is 5 to 20 μm, the magnification of the scanning electron microscope is set to 5000 times, and the imaging resolution is set to 1534×1024.
The invention provides a method for determining the particle size of a wide-distribution solid particle size standard substance of a dry dispersion system applied to a laser diffraction particle size analyzer, which is particularly used for determining the particle size of the wide-distribution solid particle size standard substance with the particle size of 1-20 mu m aiming at the dry dispersion system of the laser diffraction particle size analysis; by adopting the method for determining the value, on one hand, standard substances with representativeness and effectiveness can be obtained when the statistic quantity of particles is low, the workload of statistical analysis is greatly reduced, and on the other hand, the relative uncertainty generated in the process of determining the value can be controlled at a low level so as to meet the national standard requirements.
Drawings
FIG. 1 is a partial example of a scanning electron microscope image of the particles obtained in example 1;
FIG. 2 is a volume distribution curve as described in step a) of the simulation calculation of example 1 of the present invention;
FIG. 3 is a graph showing the relationship between the different sampling numbers L and the generated relative errors in the simulation calculation of the embodiment 1 of the present invention;
FIG. 4 is a volume distribution curve as described in step a) of the simulation calculation of example 2 of the present invention;
FIG. 5 is a graph showing the relationship between the different sampling numbers L and the generated relative errors in the simulation calculation of embodiment 2 of the present invention.
Detailed Description
The present invention will be described in detail below with reference to specific embodiments shown in the drawings. However, these embodiments are not intended to limit the present invention, and structural, methodological, or functional modifications of these embodiments are intended to be included within the scope of the present invention.
Example embodiments will now be described more fully with reference to the accompanying drawings. However, the exemplary embodiments can be embodied in many forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art.
Materials, reagents and the like used in the following examples are commercially available unless otherwise specified.
Example 1
A method for determining a wide-distribution solid particle size standard substance according to example 1, comprising the steps of, in order:
step 1): initial samples were selected: the initial sample selected was a glass bead particle product (product of "high refractive index glass beads (nd=1.93)" from the company of the directional reflector material, hendra, tsukushinai), the initial sample weight was 3kg, the sphericity of the particles was more than 95%, and the expected characteristic particle diameter D50 was around 10 microns.
In one embodiment of the present application, the ratio of the expected characteristic particle diameter D90 to D10 of the initial sample after rough measurement is 1.5 to 10; in this example, the ratio of the expected characteristic particle diameter D90 to D10 of the initial sample after rough measurement was about 2.3.
Step 2): particle sample preparation: dispersing the initial sample to prepare a particle sample in a single-particle independent and uniform dispersion state;
in a specific embodiment of the present application, the particle sample preparation of step 2) comprises a spin-fork shrinkage operation and a high pressure dispersion operation;
the operation of the rotary cross-division is as follows: adopting a dry powder disperser to carry out rotary cross shrinkage on the initial sample selected in the step 1), wherein the mass of the obtained separated sample is 0.01 g-0.05 g;
the operation of the high pressure dispersion is as follows: and placing the separated samples in a sample groove arranged at the upper part of the closed space, dispersing the particles of the separated samples into a plurality of round holes uniformly distributed around the sample groove in a high-pressure spraying mode, and freely settling the round holes on a sample table below to obtain the particle samples with single particles independent and in a uniform dispersion state.
In one embodiment of the present application, step 1) the initial product selected is scaled down step by step to 10 g/bottle using rotary cross-scaling, controlling the relative uncertainty contributed by the inter-bottle non-uniformity of the particle characteristic particle size D50 values between each bottle, randomly selecting 1 bottle, and continuing rotary cross-scaling to 0.01 g-0.05 g.
In particular, in this example, the relative uncertainty contributed by the inter-bottle unevenness of controlling the value of the particle characteristic particle diameter D50 between each bottle was equal to or less than ±0.5%.
In particular, in this example, the mass of the divided sample obtained after the rotary cross-division was about 0.02g.
In this embodiment, in the high-pressure dispersing operation, the sample tank is communicated with a high-pressure gas source (generally He gas), and particles of the sub-sample are uniformly dispersed to surrounding circular holes by high-pressure spraying.
In a specific embodiment of the present application, the ratio of the diameter of the sample tank, the diameter of the plane formed by the plurality of round holes and the diameter of the plane on which the particle sample is distributed on the sample stage is 1:2: 6-1: 3:9, a step of performing the process; the ratio of the planar diameter of the particle sample distribution on the sample table to the height of the closed space is 1:1 to 1:2.
in a more preferred embodiment of the present application, the diameter of the circular hole ranges from 1 to 5mm.
In this embodiment, the mass of the sample on the sample tank is 0.02g, the diameter of the sample tank is about 1cm, the distance from the center of the sample tank to the center of the round hole is about 1.3cm, and the pressure of the high-pressure spray is about 4 bar; the diameter of the round hole is about 3mm; the distance between the circle centers of adjacent round holes is about 2.3 times of the diameter of the round holes; the number of the round holes is 12; the vertical height from the round hole to the sample table is 12cm; after high-pressure spraying, the particles of the sub-sample are uniformly dispersed to surrounding round holes, fall freely from the round holes and are settled to a sample stage, and finally the plane diameter range of the plane diameter of the particle sample distribution on the sample stage is about 8cm.
On the basis of knowing the above parameter characteristics, the skilled person can adjust the high-pressure injection pressure according to the mass and volume of the sample, the distribution size of the sample groove and the distance between the center of the sample groove and the center of the round hole, and in a word, the particles falling on the sample table are ensured to be in a state that single particles are independent and uniformly dispersed.
Step 3): estimating: obtaining the estimated particle size distribution data of the particle sample prepared in the step 2);
the estimated particle size distribution data is obtained by artificial assumption or experimental means;
the estimated particle size distribution data includes an estimated characteristic particle size D50, an estimated particle size distribution range, and a corresponding particle size standard deviation thereof.
In a specific embodiment of the present application, the estimated particle size distribution data is obtained by experimental means; the experimental means is that a laser diffraction particle size analyzer is adopted for rough measurement to obtain the estimated particle size distribution data, or a scanning electron microscope is adopted for randomly obtaining particle images, and image processing is carried out to obtain the estimated particle size distribution data.
In this embodiment, a scanning electron microscope is used to randomly acquire a particle image, and image processing is performed to obtain the estimated particle size distribution data.
Step 4): simulating and calculating a representative minimum particle statistics value required for obtaining a fixed value;
the simulation calculation comprises the following steps:
step a): performing Gaussian fitting on the estimated particle size distribution data to obtain a corresponding volume distribution curve;
step b): setting the total volume of the particle sample prepared in the step 2) as V, and dividing the volume distribution curve into equal n parts of subintervals; in each subinterval i (i= … n), the particle size values in the interval are repeatedly and randomly generated until the sum of the volumes corresponding to the particle size values in the interval reaches the theoretical volume V occupied by the particle size interval i At this time, the number of particle diameter values in each sub-interval is N i ；
Step c): combining the particle size values of each subinterval to form a simulation sampling pool with the number of N, randomly taking L particle size values from the simulation sampling pool, and carrying out statistical analysis on the L particle size values to obtain a corresponding simulation statistical characteristic particle size D50;
step d): comparing the simulated statistical particle size D50 obtained in step c) with the estimated characteristic particle size D50 and calculating an error; when the fluctuation range of the error value is +/-0.3-0.4%, the corresponding minimum L value is the representative minimum particle statistics value required by the fixed value.
In this embodiment, matlab software is adopted for simulation calculation, and the specific calculation process is as follows:
step a): estimated characteristic particle diameters d50= 10.2917 micrometers, d10= 7.2067 micrometers and d90= 12.8546 micrometers, standard deviation=2.0, corresponding volume distribution curves were obtained, see fig. 2;
step b): the total volume of the particle population of the selected sample was set to V (in this example, total volume v=4.6x10 8 Cubic micrometers), dividing the volume distribution curve into equal n sub-regions (in particular, in this embodiment, n is selected to be 1000); in each subinterval i (i= … n), repeatedly and randomly generating the particle size value in the interval by software until the sum of the volumes corresponding to the particle size values in the interval reaches the theoretical volume V occupied by the particle size interval i At this time, the number of particle diameter values in each sub-interval is N i ；
Step c): combining the particle size values of each subinterval to form a simulation sampling pool with the number of N; in this embodiment, a simulation sampling pool of n=100 tens of thousands is obtained from the volume distribution curve;
l particle size values are randomly taken from the particle size distribution table, and then the L particle size values are subjected to statistical analysis to obtain corresponding simulation statistical characteristic particle size D50;
step d): comparing the simulated statistical particle size D50 obtained in step c) with the estimated characteristic particle size D50 and calculating an error; when the fluctuation range of the error value is +/-0.3-0.4%, the corresponding minimum L value is the representative minimum particle statistics value required by the fixed value.
Changing the value of L, for example 1 thousand, 2 thousand, 3 thousand, 1 ten thousand, 2 ten thousand, 10 ten thousand, repeating the operations of step c) and step d).
Referring to fig. 3, the relative errors resulting from different sampling numbers L are shown; as can be seen from the graph, in this embodiment, the minimum L value corresponding to the fluctuation range of the error value of about ±0.3 to 0.4% is about 2 ten thousand, which is the representative particle statistics value required for the determination in step 5).
Step 5) scanning imaging, statistics and analysis:
scanning electron microscopy was used to image the particle sample prepared in step 2).
And (3) measuring the diameters of the particles imaged by scanning one by adopting an internal standard method, and carrying out statistical analysis according to the minimum particle statistics value obtained in the step (4) to obtain the actual particle size distribution and particle characteristic particle size D50 and the measurement uncertainty corresponding to the particle characteristic particle size D50.
For a wide-distribution solid granularity standard substance, the relative uncertainty of a fixed value mainly comes from several aspects, and [1] the length of a grid grating for scanning electron microscope calibration is relatively uncertainty; [2] when shooting particles, the magnification of a scanning electron microscope is increased; [3] imaging resolution of a scanning electron microscope during particle shooting; [4] setting a digital image pixel threshold value during particle measurement; [5] particle distribution width; [6] participating in counting the number of particles; [7] non-uniformity among the sub-packaging bottles; [8] instability in long-term storage.
Regarding items [1], [7] and [8], without being related to the method of determining the value of the present application, a default value contributing to the relative uncertainty is set according to the conventional knowledge of those skilled in the art. Specifically in this example, the expected particle characteristic diameter D50 of the initial sample selected is 10 microns, it being desirable to be able to control the overall constant uncertainty thereof to a level of less than 2%; thus, the relative uncertainty contributed by the non-uniformity among bottles of the split charging of item [7] was set to 0.5%, and the relative uncertainty contributed by the instability of the long-term storage of item [8] was set to 0.5%. With respect to item [1], in this embodiment, the scanning electron microscope is calibrated with grid grating pixels, and the range of relative uncertainty contributed by the selected grid grating length is less than or equal to 0.5%.
The inventor of the application finds that, through a great deal of experimental research, the wide-distribution solid granularity standard substance, especially the wide-distribution solid granularity standard substance with the particle diameter smaller than 20 microns, applied to a dry dispersion system of a laser diffraction particle size analyzer is very critical in a simulation calculation process, and can obtain a representative and effective standard substance with a lower particle statistics quantity by simulating calculation to obtain a representative minimum particle statistics value required by a fixed value, thereby greatly reducing the workload of statistical analysis, and more importantly, controlling the relative uncertainty generated in a fixed value process to be at a lower level.
In addition, parameter control of the magnification and imaging resolution of a scanning electron microscope is important.
In one embodiment of the present application, the relative uncertainty of particle size measurement due to magnification and imaging resolution of a scanning electron microscope is shown in table 2 when the expected particle size is 10 microns.
TABLE 2
In one embodiment of the present application, the imaging resolution is 1536×1024 when the estimated characteristic particle diameter D50 is 1 to 5 μm, the magnification of the scanning electron microscope is 20000 times.
In another embodiment of the present application, the scanning electron microscope is at 5000 x magnification and imaging resolution is 1534 x 1024 when the estimated characteristic particle diameter D50 is 5 to 20 microns.
In particular, in this example, the expected characteristic particle diameter D50 of the particle sample was about 10 μm, the magnification of the scanning electron microscope was 5000 times, and the imaging resolution was 1534×1024.
Referring to fig. 1, an example of a scanning electron microscope (part of) the particles obtained in example 1 is shown.
Specifically, in this embodiment, the diameter of the particles imaged by scanning is measured one by using an internal standard method, and statistical analysis is performed according to the minimum particle statistics value (2 ten thousand) obtained in the step 4), so as to obtain the actual particle characteristic particle diameter d50=10.3 micrometers.
For the constant value method of example 1 of the present application, the inventors calculated the relative uncertainty, and the results are shown in table 3 below.
TABLE 3 Table 3
And (3) notes: the calculation formula of the composite relative uncertainty is as follows:
the calculation formula of the extended relative uncertainty is: u (U) 95 ＝2*u crel (x)(k＝2)
As can be seen from the above Table 3, the wide-distribution solid particle size standard substance having a particle size of less than 20 μm obtained by the constant value method of example 1 has an expanded relative uncertainty of 2.0% as produced in the above items [1] to [8 ].
The method of the embodiment 1 can effectively estimate and greatly reduce the relative uncertainty generated in the [2] to the [6], and is convenient for controlling the total relative uncertainty at a lower level so as to meet the national specification requirement.
Example 2
A method for determining a wide-distribution solid particle size standard substance according to example 2, comprising the steps of, in order:
step 1): initial samples were selected: 10g of a 1 kg glass bead particle product (product of "high refractive index glass beads (nd=1.93)" from Jiangxi Shengfu light retroreflective materials Co., ltd.) having a sphericity of the particles of more than 95% and a characteristic particle diameter D50 of about 3 μm and a ratio of the characteristic particle diameter D90 to D10 of about 1.6 was randomly selected as the initial sample of example 2.
Step 2): particle sample preparation: dispersing the initial sample selected in the step 1) to prepare a particle sample in a single particle independent and uniform dispersion state;
in this example, the particle sample preparation of step 2) includes an operation of rotary cross-division and an operation of high pressure dispersion;
wherein the operation of rotating cross-division is: performing rotary cross-shrinkage on the initial sample selected in the step 1) by adopting a dry powder disperser; specifically, the rotary cross-shrinkage is adopted to gradually shrink to 10 g/bottle, the relative uncertainty (for example, the relative uncertainty is less than or equal to +/-0.5%) contributed by the inter-bottle nonuniformity of the particle characteristic particle size D50 value among each bottle is controlled, 1 bottle is randomly selected, and the rotary cross-shrinkage is continued to reach 0.01g.
Wherein the high pressure dispersing operation is as follows: and placing the separated samples in a sample groove arranged at the upper part of the closed space, dispersing the particles of the separated samples into a plurality of round holes uniformly distributed around the sample groove in a high-pressure spraying mode, and freely settling the round holes on a sample table below to obtain the particle samples with single particles independent and uniformly dispersed.
In this embodiment, in the high-pressure dispersing operation, the sample tank is communicated with a high-pressure gas source (generally He gas), and particles of the sub-sample are uniformly dispersed to surrounding circular holes by high-pressure spraying.
The sample groove is communicated with a high-pressure gas source (generally adopting He gas), and particles of the sub-sample are uniformly dispersed to surrounding round holes in a high-pressure spraying mode.
In this embodiment, the mass of the sample on the sample tank is 0.01g, the diameter of the sample tank is about 0.7cm, the distance from the center of the sample tank to the center of the round hole is about 2cm, and the pressure of high-pressure injection is about 3bar; the diameter of the round hole is about 2mm; the distance between the circle centers of adjacent round holes is about 2 times of the diameter of the round hole; the vertical height from the round hole to the sample table is 10cm; after high-pressure spraying, the particles of the sub-sample are uniformly dispersed to surrounding round holes, freely fall from the round holes and sink to the sample stage, and finally the diameter range of the plane of the particle distribution on the sample stage is about 7cm.
Step 3): estimating: obtaining the estimated particle size distribution data of the particle sample prepared in the step 2);
the estimated particle size distribution data is obtained by artificial assumption or experimental means;
the estimated particle size distribution data includes an estimated characteristic particle size D50, an estimated particle size distribution range, and a corresponding particle size standard deviation thereof.
In this embodiment, the estimated particle size distribution data is obtained by rough measurement using a particle size analyzer using a laser diffraction method.
Step 4): simulating and calculating a representative minimum particle statistics value required for obtaining a fixed value;
in this embodiment, matlab software is adopted for simulation calculation, and the specific calculation process is as follows:
step a): estimated characteristic particle diameters d50= 2.9976 micrometers, d10= 2.3510 micrometers and d90= 3.6330 micrometers, standard deviation=0.5, corresponding volume distribution curves were obtained, see fig. 4;
step b): the total volume of the particle population of the selected sample was set to V (in this example, total volume v=4.6x10 7 Cubic micrometers), dividing the volume distribution curve into equal n sub-regions (in particular, in this embodiment, n is selected to be 1000); in each subinterval i (i= … n), repeatedly and randomly generating the particle size value in the interval by software until the sum of the volumes corresponding to the particle size values in the interval reaches the theoretical volume V occupied by the particle size interval i At this time, the number of particle diameter values in each sub-interval is N i ；
Step c): combining the particle size values of each subinterval to form a simulation sampling pool with the number of N; in this embodiment, a simulation sampling pool of n=100 tens of thousands is obtained from the volume distribution curve;
l particle size values are randomly taken from the particle size distribution table, and then the L particle size values are subjected to statistical analysis to obtain corresponding simulation statistical characteristic particle size D50;
step d): comparing the simulated statistical particle size D50 obtained in step c) with the estimated characteristic particle size D50 and calculating an error; and when the fluctuation range of the error value is +/-0.3-0.4%, the corresponding minimum L value is the particle statistics value.
Changing the value of L, for example 1 thousand, 2 thousand, 3 thousand, 1 ten thousand, 2 ten thousand, 10 ten thousand, repeating the operations of step c) and step d).
Referring to fig. 5, the relative errors resulting from different sampling numbers L are shown; as can be seen from the graph, in this embodiment, the minimum L value corresponding to the fluctuation range of the error value of about ±0.3 to 0.4% is about 4 ten thousand, which is the representative particle statistics value required for the determination in step 5).
Step 5) scanning imaging, statistics and analysis:
scanning electron microscopy was used to image the particle sample prepared in step 2).
In this embodiment, the scanning electron microscope is calibrated by using grid pixels, and the relative uncertainty range of the grid length is less than 0.5%;
in particular, in the present embodiment, the expected characteristic particle diameter D50 of the particles on the sample stage is about 3 μm, the magnification of the scanning electron microscope is 20000 times, and the imaging resolution is 1534×1024.
In one embodiment of the present application, the relative uncertainty of particle size measurement due to magnification and imaging resolution of a scanning electron microscope is shown in table 4 when the particle size is 3 microns.
TABLE 4 Table 4
| Magnification ratio | Resolution setting | 3 mu m particleParticle measurement uncertainty% |
| 20000X | 1536*1024 | 0.447 |
Specifically, in this embodiment, the diameter of the particles imaged by scanning is measured one by using an internal standard method, and statistical analysis is performed according to the minimum particle statistics value (4 ten thousand) obtained in the step 4), so as to obtain the actual particle characteristic particle diameter d50=3.1 micrometers.
For the constant value method of example 2 of the present application, the inventors calculated the relative uncertainty, and the results are shown in table 5 below.
TABLE 5
And (3) notes: the calculation formula of the composite relative uncertainty is as follows:
the calculation formula of the extended relative uncertainty is: u (U) 95 ＝2*u crel (x)(k＝2)
As can be seen from Table 5, the wide-distribution solid particle size standard substance having a particle size of less than 5. Mu.m, which is obtained by the constant value method of example 2, has a relative uncertainty of expansion of less than 2.0% in the above items [1] to [8 ].
By adopting the method for setting the value in the embodiment 2, the relative uncertainty generated in the items [2] to [6] can be effectively estimated and greatly reduced, and the total relative uncertainty can be conveniently controlled at a lower level so as to meet the national specification requirement.
In summary, the inventors of the present application have improved the method for determining the value of the standard substance of the wide-distribution solid particle size of the small particle size (particle size smaller than 20 μm) applied to the dry dispersion system of the laser diffraction particle size analyzer, on the one hand, the representative minimum particle statistics value required for obtaining the value through the simulation calculation can greatly reduce the workload of the statistical analysis, and more importantly, can control the relative uncertainty generated in the whole determination process to a lower level.
It should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is for clarity only, and that the skilled artisan should recognize that the embodiments may be combined as appropriate to form other embodiments that will be understood by those skilled in the art.
The above list of detailed descriptions is only specific to practical embodiments of the present invention, and they are not intended to limit the scope of the present invention, and all equivalent embodiments or modifications that do not depart from the spirit of the present invention should be included in the scope of the present invention.
Claims (8)
1. A method for determining the standard substance of wide-distribution solid granularity of dry dispersing system applied to laser diffraction granularity analyzer is characterized by that,
the constant value method comprises the following steps in sequence:
step 1): initial samples were selected: the initial sample is selected to be glass microsphere particles, the sphericity of the particles is more than 95%, the expected characteristic particle diameter D50 is 1-20 microns, and the ratio of the expected characteristic particle diameter D90 to the expected characteristic particle diameter D10 is 1.5-10;
step 2): preparation of particle samples: dispersing the initial sample to prepare a particle sample in a single-particle independent and uniform dispersion state;
step 3): estimating: obtaining the estimated particle size distribution data of the particle sample prepared in the step 2);
the estimated particle size distribution data is obtained by artificial assumption or experimental means;
the estimated particle size distribution data comprises an estimated characteristic particle size D50, an estimated particle size distribution range and a corresponding particle size standard deviation;
step 4): simulating and calculating a representative minimum particle statistics value required for obtaining a fixed value;
the simulation calculation comprises the following steps:
step a): performing Gaussian fitting on the estimated particle size distribution data to obtain a corresponding volume distribution curve;
step b): setting the total volume of the particle sample prepared in the step 2) to beVDividing the volume distribution curve into equalnA sub-interval; in each subintervaliRepeatedly and randomly generating the particle size value in the interval until the sum of the volumes corresponding to the particle size values in the interval reaches the theoretical volume occupied by the particle size interval Vi At this time, the number of particle diameter values in each sub-interval is Ni Whereini=1…n；
Step c): combining the particle size values of each subinterval to form a number ofNIs randomly taken from the simulation sampling poolLParticle size value, and then to thisLCarrying out statistical analysis on the particle size values to obtain corresponding simulated statistical characteristic particle size D50;
step d): comparing the simulated statistical characteristic particle diameter D50 obtained in the step c) with the estimated characteristic particle diameter D50, and calculating an error; the minimum corresponding to the fluctuation range of the error value is + -0.4%LThe value is the minimum particle statistics value;
step 5) scanning imaging, statistics and analysis:
scanning and imaging the particle sample prepared in the step 2) by using a scanning electron microscope;
and (3) measuring the diameters of the particles imaged by scanning one by adopting an internal standard method, and carrying out statistical analysis according to the minimum particle statistics value obtained in the step (4) to obtain the actual particle size distribution and particle characteristic particle size D50 and the measurement uncertainty corresponding to the particle characteristic particle size D50.
2. The method of calibrating according to claim 1, wherein:
the particle sample preparation of step 2) includes a rotary cross-division operation and a high-pressure dispersion operation;
the operation of the rotary cross-division is as follows: adopting a dry powder disperser to carry out rotary cross shrinkage on the initial sample selected in the step 1), wherein the quality of the obtained separated sample is 0.01 g-0.05 g;
the operation of the high pressure dispersion is as follows: and placing the separated samples in a sample groove arranged at the upper part of the closed space, dispersing the particles of the separated samples into a plurality of round holes uniformly distributed around the sample groove in a high-pressure spraying mode, and freely settling the round holes on a sample table below to obtain the particle samples in a single-particle independent and uniform dispersion state.
3. The method of thresholding of claim 2, wherein:
and 1 bottle is randomly selected, and the rotary cross shrinkage is continuously carried out until the relative uncertainty contributed by the inter-bottle nonuniformity of the particle characteristic particle diameter D50 value among each bottle is 0.01 g-0.05 g.
4. The method of thresholding of claim 2, wherein:
the ratio of the diameter of the sample groove to the diameter of a plane formed by the circular holes to the diameter of the plane on which the particle samples are distributed on the sample table is 1:2: 6-1: 3:9, a step of performing the process;
the ratio of the planar diameter of the particle sample distribution on the sample table to the height of the closed space is 1: 1-1: 2.
5. The method of calibrating according to claim 4, wherein:
the diameter range of the round hole is 1-5 mm.
6. The method of calibrating according to claim 5, wherein:
in the step 1), selecting a range of 8-12 microns of expected characteristic particle diameter D50 of the sample;
in the step 3), the diameter of the round hole is 2-4 mm; the diameter of the sample groove is 0.8-1.2 cm; the number of the round holes is 11-13;
the injection pressure of the high-pressure injection is 3-5 bar;
the vertical height from the round hole to the sample table is 11-13 cm; the diameter range of the plane of the particle sample distribution on the sample table is 7-9 cm;
in the step 5), the magnification of the scanning electron microscope is 5000 times, and the imaging resolution is 1534×1024.
7. A method of calibrating according to any of claims 1 to 6, wherein:
the estimated particle size distribution data are obtained through experimental means; the experimental means is that a laser diffraction particle size analyzer is adopted for rough measurement to obtain the estimated particle size distribution data, or a scanning electron microscope is adopted for randomly obtaining particle images, and image processing is carried out to obtain the estimated particle size distribution data.
8. A method of calibrating according to any of claims 1 to 6, wherein:
in the step 5), when the estimated characteristic particle diameter D50 is 1 to 5 μm, the magnification of the scanning electron microscope is set to 20000 times, and the imaging resolution is set to 1536×1024;
when the estimated characteristic particle diameter D50 is 5 to 20 micrometers, the magnification of the scanning electron microscope is set to 5000 times, and the imaging resolution is set to 1534×1024.
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