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マイクロトラック・ベル

capital6580Ten thousand
number of employees120
addressOsaka/Suminoe-ku, Osaka-shi/2-52, Higashi 8-chome, Nangang
phone06-6655-0362
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last updated:Jun 12, 2023
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High-precision gas adsorption measurement device "BELSORP MAX G"

Demo/analysis now available. Compact and low-cost! Dedicated equipment capable of evaluation from micro pores (activated carbon, zeolite, MOF, etc.).

"BELSORP MAX G" is a compact and low-cost gas adsorption measurement device within the BELSORP MAX series. It is a dedicated instrument capable of measuring gas adsorption isotherms from extremely low pressures for the evaluation of porous and non-porous materials with micro, meso, and macro pores. It is equipped with one measurement port, one dedicated port for measuring saturation vapor pressure, and one reference port, each with its own dedicated pressure sensor, allowing for high-precision measurements. 【Features】 ■ Evaluation from micro pores is possible through N2 and Ar ultra-low pressure isotherm measurements with the highest level of reproducibility. ■ Ultra-micropore evaluation is possible through CO2 adsorption. ■ Low specific surface area measurement through Kr adsorption. ■ Measurement of adsorption isotherms and adsorption rates for H2, CO2, O2, CH4, and non-corrosive gases. *For more details, please refer to the PDF document or feel free to contact us.

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Specific surface area/pore distribution measurement device 'BELSORP MINI X'

Demo/analysis now available. Significantly reduced measurement time and 10 times improved measurement accuracy compared to conventional products. Surface area evaluation without the need for He gas. Applicable to battery materials, ceramics, and more.

The "BELSORP MINI X" is a product capable of measuring the specific surface area and pore distribution of various functional materials, as well as adsorption isotherms of various gases from low to high temperatures. It offers world-class reproducibility through AFSM and significantly reduces measurement time with GDO. The reproducibility is extremely high, with a measurement limit improved by more than ten times compared to conventional products. Equipped with four sample measurement ports, it features high-throughput capabilities such as multi-device control. 【Features】 ■ Achieves simultaneous short-time measurement of up to 4 samples with world-class reproducibility ■ Specific surface area measurement range ・0.01 m²/g or more (N2): Reproducibility of total surface area of 10 m² ±0.4% *For more details, please refer to the PDF document or feel free to contact us.

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High-Precision Gas and Vapor Adsorption Measurement Device "BELSORP Series" Catalog

Demo/analysis currently accepted: Specific surface area/pore distribution "BELSORP MINI X" high-precision gas/vapor adsorption measurement "BELSORP MAX series," etc.

This catalog introduces the high-precision gas and vapor adsorption measurement devices of the "BELSORP series," which are suitable for evaluating the specific surface area, pore distribution, and surface characteristics of various functional materials. It features the "BELSORP MINI X," a specific surface area/pore distribution measurement device capable of simultaneous measurement of up to four samples, as well as high-precision gas adsorption measurement devices such as "BELSORP MAX G" and "BELSORP MAX." Please use this information for product selection. [Contents (excerpt)] ■ Evolution and basic principles (constant volume method) of the BELSORP series; features ■ BELSORP MINI X ■ BELSORP MAX G ■ BELSORP MAX II ■ BELSORP MAX *For more details, please refer to the PDF document or feel free to contact us.

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[Technical Information] Method of Representing Pore Distribution Graphs

Clearly distinguish between area distribution and volume distribution, and in what applications should each distribution be used?

There are several types of methods to express pore distribution. They show different distributions, but all have correct physical meanings. Here, we assume a cylindrical pore model. There is a pore with a radius of r and a length of L. On our website, we mathematically solve the formulas representing the lateral area and volume of this pore, as well as the vertical axis representation of the pore distribution. Additionally, we provide a graph analyzing the nitrogen adsorption isotherm from the adsorption side of the BAM-PM-103 standard sample using the BJH method, along with a detailed introduction. Please take a look. *For more details, please refer to the related links or feel free to contact us.*

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Technical Information: Adsorption-Desorption Isotherm Hysteresis

Should the pore distribution from the gas adsorption isotherm use the isotherm from the adsorption side or the desorption side?

From the past to the present, there has been discussion on whether to use the adsorption or desorption isotherm for pore distribution from gas adsorption. This adsorption-desorption hysteresis is thought to be due to a stepwise desorption mechanism (percolation) caused by interconnected pores of different diameters, and caution is required when analyzing pore distribution from the desorption side. Generally, it is said that pore distribution analyzed from the adsorption side is less problematic and closer to the true value. Our website provides detailed information using diagrams and tables. Please take a look. *For more details, please refer to the related links or feel free to contact us.*

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Technical Information: NLDFT/GCMC Method

Improving the reliability of pore distribution evaluation in the micro-pore region! An introduction to the NLDFT/GCMC method.

The "non-local density functional theory" and "computer simulation method" have recently developed as new evaluation methods for pore distribution in porous materials. This theory explains the adsorption of many materials and adsorbates and has been utilized for the analysis of pore distribution in micropores and mesopores. This new pore distribution evaluation method allows for the analysis of pore distribution across the entire range using a single theory, which was previously differentiated between mesopores and micropores. Additionally, it has improved the accuracy of pore distribution in the micropore region, which was previously lacking in reliability. The characteristic of these theories is that, unlike classical pore distribution analysis theories that assumed the adsorbed phase within the pores to be in a liquid state (Kelvin theory), they analyze the periodic changes in adsorption density from the solid surface. Our website provides a detailed introduction using diagrams. Please take a look. *For more details, please refer to the related links or feel free to contact us.*

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Technical Information: Meso-Macro Pore Analysis

Information on particle analysis and particle analysis devices! Introduction to meso-macro pore analysis.

The analysis theories for mesopores include BJH, CI, DH methods (cylindrical type), and Innes method (slit type). These are calculated based on the capillary condensation theory (Kelvin equation) and are generally applicable to pore diameters of 2 nm or larger. We provide detailed information on our website. Additionally, we have published a table showing the relationship between relative pressure and pore radius. Please take a look. *For more details, please refer to the related links or feel free to contact us.*

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Technical Information: Microhole Analysis

A reliable micro-pore analysis method using nano-order adsorbed molecules as probes!

The theories for analyzing micropores include t-plot, HK, SF, DR-plot, NLDFT, and GCMC methods. t-plot and DR-plot are used to calculate pore volume and internal/external specific surface area, while HK, SF, NLDFT, and GCMC are effective methods for calculating micropore distribution. Micropore analysis theory is not as straightforward as adsorption theories for planar adsorption or mesopores, due to the short distance between pore walls and adsorbed molecules. Pore shapes are assumed to be cylindrical or slit-like, and it is necessary to select atomic or adsorbate parameters for the pore walls. We provide detailed information on our website. Please take a look. *For more details, please refer to the related links or feel free to contact us.*

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Technical Information: The Relationship Between Gas Adsorption and Pore Diameter

Why can pore distribution be determined from adsorption isotherms? An introduction to the relationship between gas adsorption and pore diameter.

Within the pores, gas molecules are influenced by the attractive forces from the surrounding pore walls, and condensation within the pores begins at a pressure lower than that of the flat surface. This condensation pressure is related to the pore diameter. On our website, we provide detailed information on the relationship between adsorption isotherms and pore diameter using diagrams and tables. Please take a look. *For more details, please refer to the related links or feel free to contact us.*

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Technical Information: Pore Size Distribution Measurement Method

Introduction to pore size distribution measurement methods such as "gas adsorption method" and "mercury porosimeter"!

Typical measurement methods for the pore distribution of powders and functional materials include gas adsorption methods and mercury porosimetry. The "gas adsorption method" primarily analyzes N2 or Ar gas adsorption isotherms at low temperatures (liquid nitrogen or liquid argon), allowing for the measurement of pore diameters ranging from molecular size to several hundred nanometers. The "mercury porosimeter" is a method that involves applying pressure to mercury, which is not easily wetting to the material, and determining the pore distribution from the amount forced into the sample. Additionally, in recent years, methods such as "gas permeation" and "bubble point method" have been developed to measure only the permeable pores of filters and separation membranes. For more details, please visit our website. *For more information, please refer to the related links or feel free to contact us.

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[Technical Information] Definition of Pore Diameter

Introduction to the definition of pore diameter in nanoporous materials.

Until now, pore size has been defined as shown in the image. In 2015, IUPAC was revised, eliminating the previous subdivisions and defining it as NANOPORE (up to 100 NM). *For more details, please refer to the related links or feel free to contact us.

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Technical Information: Measurement of Small Surface Area Using KR Gas

Why is Kr used for low specific surface area evaluation?

Can low specific surface area be measured using Kr? The adsorption cross-sectional area of Kr (0.202 nm²) is 25% larger than that of N2 (0.162 nm²), making it unsuitable for measuring low specific surface area. The reason lies in the adsorption temperature and vapor pressure. In the constant volume method, the amount of gas adsorbed is calculated from the difference between the amount of gas introduced and the amount of gas that was not adsorbed. We provide detailed information on our website. Please take a look. *For more details, please refer to the related links or feel free to contact us.*

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[Technical Information] Measurement of Specific Surface Area of Samples with Micropores

What is the problem and how should we proceed? An introduction to the measurement of specific surface area of samples with micro-pores.

The BET paper states that BET theory should not be applied to Type I isotherms. However, in terms of material evaluation, specific surface area is an important parameter, and specific surface area is often calculated for materials with micropores. So what is the problem, and what should be done? Our website introduces this using diagrams and graphs. Please take a look. *For more details, please refer to the related links or feel free to contact us.*

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Technical Information: BET Theory

The theory of monolayer adsorption has been extended to multilayer adsorption! Here is a basic introduction to the evaluation method of BET specific surface area.

The specific surface area is usually analyzed using the BET theory (Brunauer-Emmett-Teller theory) from gas adsorption isotherms. The BET theory models the adsorption process starting from strong adsorption sites on the solid surface, and as the pressure increases, adsorption occurs on the next strongest sites. It also models the simultaneous occurrence of adsorption in the second and third layers. Our website presents this information using diagrams and graphs. Please take a look. *For more details, please refer to the related links or feel free to contact us.*

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Technical Information: Specific Surface Area and Particle Diameter

Samples with the same weight and actual volume can have different surface areas! An introduction to specific surface area and particle diameter.

As the particle size decreases, the specific surface area increases, and naturally, if there are pores in the particles, the specific surface area will also increase. This is important in processes and reactions, as the amount of surface sites and adsorption capacity can change even for the same material (per weight or per volume). Measuring the specific surface area is an important parameter for understanding the activity and adsorption capacity of materials (such as adsorbents and catalysts). On our website, we provide diagrams illustrating the relationship between particle size and surface area. Please take a look. *For more details, please refer to the related links or feel free to contact us.*

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Technical Information: Achieved Vacuum Level

The accuracy of adsorption isotherm measurements at ultra-low pressure has improved, enhancing the reliability of micropore analysis!

The importance of adsorption isotherm measurements under ultra-high vacuum conditions is increasing in the analysis of micro-pores and surface analysis. Currently, it is technically possible to achieve a clean vacuum, as represented by turbo molecular pumps, but it is difficult to reach high vacuum in the sample section due to the multiple valves, piping, and joints of the volumetric gas adsorption apparatus. The figure shows the difference in the exhaust gases of solenoid valves and air-operated valves. We provide detailed information on our website, so please take a look. *For more details, please refer to the related links or feel free to contact us.

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Technical Information: Free Space Measurement Method

There is no need to maintain the liquid level, and continuous measurement of free space changes is possible even during gas adsorption measurements!

The free space (dead volume) is not a geometric volume, but a convenient volume for calculating the amount of adsorption. To achieve physical adsorption, when the sample tube is cooled with a refrigerant such as liquid nitrogen, two temperature regions are created, and the gas density in this cooling section is affected by the cooling temperature and the changes in the level of the refrigerant during measurement. We provide detailed information on our website, so please take a look. *For more details, please refer to the related links or feel free to contact us.

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Technical Information: Adsorption Measurement Method

We will introduce methods that can measure adsorption quantity in a short time and are often used for quality control of materials!

Methods for measuring adsorption isotherms include the constant volume method, gravimetric method, pulse adsorption method, and flow method, with the constant volume method being primarily used for measuring specific surface area and pore distribution. Our website provides detailed information about the "constant volume method" and the "pulse adsorption method/flow method." Please take a look. *For more details, please refer to the related links or feel free to contact us.*

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Technical Information: Adsorption Isotherm

Measured a higher adsorbate density than in the gas phase! Introduction to adsorption isotherms.

A graph that measures the changes in pressure and adsorption amount while keeping the material at a constant temperature is called an "adsorption isotherm." Generally, the horizontal axis represents the relative pressure (P/P0), which is the equilibrium pressure divided by the saturation vapor pressure, taking values from 0 to 1. At P/P0 < 1, it indicates that the adsorbed gas condenses within the sample tube, meaning that the adsorption isotherm begins to show the interaction forces between the solid and the adsorbed molecules at pressures lower than the saturation vapor pressure, leading to adsorption and condensation, and it measures a higher adsorption density than in the gas phase. Additionally, in the constant volume method, the amount of adsorption is typically expressed in V/ml (STP) g-1, representing the volume of gas at standard conditions (0 °C, 1 atm). *For more details, please refer to the related links or feel free to contact us.*

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【Technical Information】What is adsorption?

Adsorption technology has been researched for a long time and is also applied in industrial processes such as gas separation!

Today, adsorption technology is also applied in industrial processes such as gas separation. Adsorption has forms as shown in the diagram, and what is unclear is the difference between chemical adsorption and physical adsorption. Generally, when a gas molecule is adsorbed onto a material and has a strong bond (such as hydrogen bonds or acid-base interactions) that cannot be desorbed at the adsorption temperature or room temperature, it is called chemical adsorption. In contrast, physical adsorption is primarily due to van der Waals forces, and desorption is possible by vacuum evacuation. Currently, it is also recommended to stop using the terms physical adsorption and chemical adsorption and instead refer to them as reversible adsorption and irreversible adsorption. *For more details, please refer to the related links or feel free to contact us.*

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Measurement of laser particle size distribution of high concentration spray droplets (spray/mist).

Demo/analysis now available. Information on the multiple scattering correction method for aerosol measurement and high-concentration spray laser particle size distribution measurement is now posted!

This page provides information on the multiple scattering correction method for measuring the particle size distribution of high-concentration sprays. It is a summary of a conference presentation given at the "11th Micronization Symposium" (December 2002). (Reference: Proceedings of the 11th Micronization Society, P174) Detailed content can be viewed through the related links. [Contents] ■ Overview ■ Measurement Data ■ Summary *For more details, please refer to the related links or feel free to contact us.

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Meaning of symbols in microtrack measurement results (summary data)

I will explain the meanings of the symbols in the measurement results (summary data). You can also view frequently asked questions and their answers.

On this page, we explain the meanings of the symbols used in the microtrack measurement results (summary data). We provide explanations using formulas and tables for the Mean Volume Diameter [MV], Mean Number Diameter [MN], Mean Area Diameter [MA], and Specific Surface Area (m2/ml) [CS], among others. We have compiled frequently asked questions on this page. You can view detailed information through the related links. 【Contents (partial)】 ■[MV] Mean Volume Diameter: Volume Average Diameter ■[MN] Mean Number Diameter: Number Average Diameter ■[MA] Mean Area Diameter: Area Average Diameter ■[CS] Calculated Specific Surface Area: Specific Surface Area (m2/ml) ■[SD] Standard Deviation: Standard Deviation *For more details, please refer to the related links or feel free to contact us.

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Microtrack particle size distribution measurement device, please tell me how to interpret the measurement results.

Frequently Asked Questions: Explanation of How to Interpret Measurement Results from the Microtrack Particle Size Distribution Measurement Device!

On this page, we explain how to interpret the measurement results of the "Microtrack Particle Size Distribution Measurement Device." We provide details on what is recorded where, including "Software Version," "Heading," "Particle Size Distribution Graph," and "Summary Data." For more detailed information, you can view the related links. 【Contents】 ■ Software Version ■ Heading ■ Particle Size Distribution Graph ■ Summary Data ■ Cumulative Percent Diameter or Particle Size Percent (optional setting) ■ Channel (CH) Data ■ Measurement Conditions *For more details, please refer to the related links or feel free to contact us.

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Why can a microtrack produce results even when multiple samples are mixed?

Unique optical system design, equipped with three lasers, slit-shaped detector structure.

The shape of the microtrack detector is slit-like, extending outward from the center of the scattering angle. In the laser diffraction/scattering method, laser light is irradiated onto particles, and the scattered light containing particle size information is detected by a detector of a certain shape to determine the particle size distribution. However, depending on the shape of the detector, the particle size information will result in signals that are proportional to the square, cube, or fourth power of the particle size. Particle size distribution data is typically expressed on a volume basis proportional to the cube of the particle size, but with commonly used detectors, various corrections must be applied to display volume-based particle size distribution data. With the slit-shaped detector of the microtrack, signals proportional to the cube of the desired particle size can be directly extracted. The significant reason why only the microtrack can provide accurate data on the mixing ratio of samples lies in the difference of this detector. *For more details, please refer to the related links or feel free to contact us.*

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Why doesn't the microtrack display accuracy?

There is no absolute scale for powders.

There is no absolute scale for powders, and Microtrack does not provide accuracy specifications. One reason for this is that accuracy is generally associated with measurements of length, pressure, temperature, voltage, etc., where an absolute scale exists. However, for powders, there is no absolute scale due to factors such as sample extraction, differences between production lots, sample oxidation, agglomeration, aging changes, and shape factors. For example, particularly with latex, the particle state changes due to environmental conditions, including aging. For this reason, Microtrack does not provide accuracy specifications. "NIST" also does not provide accuracy specifications. In terms of pricing related to various scales, "NIST" is recognized as an authoritative institution worldwide and serves as the basis for traceability. Here too, regarding powders, accuracy specifications are not provided, and the particle size and particle size distribution of standard samples are expressed by indicating the degree of variation in measurement results from sample extraction using methods such as microscopy and natural sedimentation. *For more details, please refer to the related links or feel free to contact us.*

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Why are there so many sample feeders and peripheral devices for microtrucks?

To obtain reliable particle size distribution data, it is important to choose a sample circulator that matches the characteristics!

In particle size distribution measurement, the extraction of representative samples and uniform dispersion are important themes. The microtrack sample circulators offer a wide variety of options, with many features in wet systems such as USVR, Sample Delivery Controller (SDC), and LVR, and in dry systems, options like line type and feeder type. Some customers may find the selection process challenging, but each model has been designed with consideration for the characteristics of the powders. As a result, we have a wealth of delivery records. Even for the same substance, powder characteristics can vary widely. Therefore, to obtain reliable particle size distribution data, it is crucial to select sample circulators and sample conditioners that match the characteristics of each powder, along with the performance of the analytical instrument itself. Additionally, customers have various applications, including measurement of multiple sample types, automation, and distribution measurement in organic solvents. *For more details, please refer to the related links or feel free to contact us.*

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What is the effect of refractive index in particle size measurement?

Especially for particles with very small diameters, the scattering phenomenon is greatly influenced by their refractive index.

In devices that measure the light scattering of particles, such as laser diffraction and scattering particle size distribution measurement devices, the refractive index of the dispersion medium and the particles, the particle diameter, and the wavelength of the light source are important factors. As an example, the scattering light intensity due to the difference in refractive index is shown in the diagram with the particle size parameter α = πD/λ (D: particle diameter, λ: wavelength of the light source) as a variable. The scattering phenomenon changes sensitively with particle diameter and refractive index, as shown in the diagram. For large particles with low translucency, diffraction phenomena dominate the scattering phenomenon, and the influence of the refractive index is minimal. However, for small translucent particles, various phenomena that change with the refractive index, such as reflection and refraction at the particle-dispersion medium interface, light attenuation within the particle, and reflection at the inner surface of the particle, have a significant impact. *For more details, please refer to the related links or feel free to contact us.*

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What is the difference between number distribution and mass (volume) distribution in particle size measurement?

Even with the same particle size distribution, the way it is represented can greatly affect the shape of the distribution, so caution is required!

The number distribution is an image when measuring the size of particles with a microscope. In other words, it is a method of representing the number and size of particles as a distribution. In contrast, the mass (volume) distribution is an image when measuring the size of particles with a sieve. This means it is a method of representing the size of particles as a distribution of mass. Additionally, when measuring the particles by size (volume) instead of mass, it is referred to as volume distribution. Even with the same particle size distribution, the representation method (number distribution and volume distribution) can lead to significantly different shapes of the distribution, so caution is required. *For more details, please refer to the related links or feel free to contact us.*

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What kind of particle size is the volume average diameter [MV] in particle size measurement?

[MV] is the volume-weighted average diameter!

The volume average diameter refers to the "MV" value. However, it is important to note that the cumulative 50% particle diameter is often referred to as the average diameter. This cumulative 50% particle diameter should be referred to as the median or mid-diameter. Below are representative examples of characteristic values that describe the particle size distribution of powders. [10%, 50%, 90%] 10%, 50%, 90% (μm: micrometers) Assuming a collection of a powder, let’s say its particle size distribution has been determined. When the cumulative curve is obtained with the total volume of the powder population set to 100%, the particle diameters at the points where the cumulative curve reaches 10%, 50%, and 90% are referred to as the 10% diameter, 50% diameter, and 90% diameter (μm), respectively. In particular, the 50% diameter is commonly used as one of the parameters to evaluate particle size distribution as the cumulative median diameter (Median diameter). *For more details, please refer to the related links or feel free to contact us.

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What are the differences in physical properties based on particle size?

From nano to centimeter-sized powders! Various physical properties due to differences in particle diameter.

This page introduces the differences in physical properties based on particle size. We explain various physical properties resulting from differences in particle sizes ranging from nano to centimeter using tables. We compare the following items: "Particle Observation," "Light Phenomena," "Relationship between Particle Size Reduction and Increased Surface Area," "Adhesion Force," and "Others." Detailed information can be viewed through the related links. 【Item Contents】 ■ Particle Observation ■ Light Phenomena ■ Relationship between Particle Size Reduction and Increased Surface Area ■ Adhesion Force ■ Others *For more details, please refer to the related links or feel free to contact us.

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Demo/Analysis Now Accepting Mercury Porosimeter 'BELPORE Series'

Compact, high safety, automatic control! A new stage in the evaluation of porous materials.

The "BELPORE series" is a mercury porosimeter suitable for evaluating the pore structure (meso and macro pores) of porous materials. By measuring mercury intrusion from vacuum to 414 MPa, it is possible to accurately and quickly evaluate the pores of porous materials in the range of 1 mm to 3.6 nm. Furthermore, it is an advanced instrument capable of evaluating specific surface area, density, and particle size distribution. 【Features】 ■ Fully automatic vertical filling from high vacuum state ■ High-precision measurements of up to 20,000 points ■ High safety ■ Compact design for space-saving *For more details, please refer to the PDF document or feel free to contact us.

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Dynamic Light Scattering (DLS)

Particle size and zeta potential measurement! We measure fine particles in suspensions and emulsions with high precision.

Dynamic light scattering (DLS) is an established measurement technique for evaluating the particle size distribution in suspensions and emulsions. Microtrack, a pioneering presence in particle size distribution measurement technology, has been developing optical systems based on dynamic light scattering for over 30 years. Dynamic light scattering (DLS) measures microparticles in suspensions and emulsions with high precision. It can measure microparticles smaller than 100 nm, which are difficult to measure using laser diffraction and scattering methods, achieving high-precision measurements across a wide concentration range from low to high concentrations. 【Features of Dynamic Light Scattering (DLS)】 - Based on Brownian motion (small particles move quickly, while large particles move slowly) - Capable of measuring particle sizes from approximately 1 nm to several micrometers - Can measure microparticles smaller than 100 nm, which are difficult to measure with laser diffraction and scattering methods - Achieves high-precision measurements across a wide concentration range from low to high concentrations - Capable of measuring zeta potential and molecular weight *For more details, please refer to the related links or feel free to contact us.

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Laser diffraction and scattering

It is a particle size distribution measurement device that covers a wide measurement range from nm to μm to mm.

Our company is a global leader in laser diffraction devices with over 40 years of experience. We continuously improve the technology related to our devices and provide a range of laser diffraction products suitable for particle size measurement and physical property evaluation to our customers. We offer particle size and shape analysis devices such as "SYNC," as well as "MT3000II" and "AEROTRAC II." 【Product Lineup】 ■ Particle size and shape analysis device "SYNC" ■ MT3000II ■ AEROTRAC II *For more details, please refer to the related links or feel free to contact us.

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Absorption

Extinction and Adsorption

In this article, to distinguish between broad and narrow meanings, we will refer to the former as extinction and the latter as adsorption. For particle size analyzers, extinction is the more significant concept. First, let’s briefly explain absorption as a physical phenomenon. The presence of matter affects the propagation of light in various ways. This includes scattering, reflection, refraction, and the absorption we are discussing here. So why does this absorption occur? You know that light is a type of electromagnetic wave. This means that there is an oscillator with a certain frequency. *For more details, please refer to the related links or feel free to contact us.*

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Refraction and reflection

Snell's Law

Have you ever had the experience of trying to spear a fish from above the water, only to miss? This happens because the position of the fish as seen from above the water is different from its actual position. In other words, this occurs because the light coming from underwater changes direction somewhere. This is called refraction. This issue of reflection is actually an important problem for instruments that use light scattering for measurement. If the angle of the scattered light entering the surface of the cell or the lens is not carefully designed, accurate measurements cannot be made. *For more details, please refer to the related links or feel free to contact us.*

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Interference

A model of the wave surface when a stone is thrown into the water.

This characteristic is not very much related to the laser diffraction method. Interference becomes an important phenomenon in understanding the principle of nanotracks. An example of interference is the model of wave patterns when a stone is thrown into the water surface. If two stones are dropped at a distance apart on the water surface, it can be observed that when the crest of one wave meets the trough of another wave, the waves weaken, while when crests meet crests, the waves strengthen. This is interference. The first concept that comes up is a mathematical theorem called "Fourier's theorem." According to this theorem, if certain conditions are met, any function can be expressed as a sum of a finite or infinite number of sine functions. In simple terms, most waveforms can be decomposed into multiple sine curves. *For more details, please refer to the related links or feel free to contact us.*

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Equation representing the intensity distribution of the diffraction pattern.

Slit width of the opening = diameter of spherical particles

Until now, we have discussed diffraction in the context of illuminating an aperture, but for us, the manufacturers of laser diffraction particle size distribution measurement devices, it is fortunate that the same phenomenon can be observed when light is directed at the particles instead of the aperture hole. Furthermore, Mie theory is based on a single sphere, but it can also be applied to multiple spheres when the material and diameter are all equal, and they are distributed irregularly with a spacing that is sufficiently large compared to the wavelength. Conveniently for measurement device manufacturers, the amount of scattered light increases proportionally with the number of spheres. *For more details, please refer to the related links or feel free to contact us.*

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The relationship between the slit width and the diffraction light intensity pattern.

Light has wave-like properties.

I believe it is unnecessary to explain again that light has wave properties and that various optical phenomena change depending on its wavelength. Now, to organize the changes in the wavelength of light and the slit diameter that will be discussed, we will introduce parameters. λ: wavelength of light, D: slit diameter, which, as can be understood from the dimensions of the numerator and denominator, becomes a dimensionless number. As α becomes smaller, the diffraction intensity pattern of Fraunhofer diffraction mentioned earlier takes the shape shown on the right side of the figure, while as α becomes larger, it takes the shape on the left side. Now, considering λ as constant, the shapes produced will change depending on whether D is large or small. Here, I will expand a little on the equations to induce the reader's drowsiness and disguise the thin content. *For more details, please refer to the related links or feel free to contact us.*

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Fraunhofer diffraction

Interference of light using parallel light.

The diffraction theory explained by the other Fraunhofer actually serves as the fundamental theory for the particle size distribution measurement device using laser diffraction, which will be discussed later. In a very rough classification to distinguish it from Fresnel diffraction: - Fresnel diffraction occurs when both the light source and the observation point are close to the aperture where diffraction occurs. - Fraunhofer diffraction occurs when both the light source and the observation point are infinitely far from the aperture where diffraction occurs. The Fraunhofer diffraction phenomenon can be mathematically expressed more simply compared to Fresnel diffraction. For experts in optics, this may seem like a rough development akin to being struck by lightning, but for those who are eager to understand the reason behind the formation of fringes, I strongly recommend reading the reference materials on light provided in the appendix. *For more details, please refer to the related links or feel free to contact us.*

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Fresnel diffraction

Interference of secondary spherical waves

There are two teachers, Fresnel and Fraunhofer, who explained the phenomenon of diffraction. Fresnel explained this diffraction by considering the mutual interference of secondary spherical waves based on Huygens' principle, which is why it is also called the Huygens-Fresnel principle. "Each point on the wavefront at a given time acts as a source of secondary spherical waves, and the amplitude of the secondary waves decreases as the angle of inclination between the direction of the primary wave and the secondary wave increases, reaching a maximum when both waves are directed in the same direction and a minimum when they are directed in opposite directions. These phenomena arise from the mutual interference of the secondary spherical waves." *For more details, please refer to the related links or feel free to contact us.*

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Diffraction of light

Huygens' principle

One famous person who explained the behavior of light based on its rectilinearity and wave-like properties is the renowned Huygens. Huygens used the following model to explain the rectilinearity of light. Diffraction phenomena can often be observed up close among you. For example, I don't wake up very early, so I haven't seen it much, but before the sun fully appears at sunrise, the ridge of the eastern mountains can be seen glowing strongly as if outlined by light. This is the diffraction of light. *For more details, please refer to the related links or feel free to contact us.

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Mie scattering

Basis of laser diffraction and scattering devices.

G. Mie successfully handled the diffraction of plane monochromatic waves by uniform spheres of arbitrary diameter and material, which exist in a homogeneous medium, using electromagnetism in 1908, obtaining an exact solution. This scattering phenomenon is very important to us. The significance of Mie scattering lies in the fact that a considerable portion of the measurement range of the particle size distribution measurement devices we are dealing with falls within this category. However, mathematically solving Mie's scattering presents very challenging elements. Although programs have already been developed to solve Mie's equations using computers, it remains a difficult task, and how to overcome this problem becomes the know-how of particle size distribution measurement device manufacturers. *For more details, please refer to the related links or feel free to contact us.*

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Rayleigh scattering

A theory applicable to scattered light from particles much smaller than the wavelength of laser light.

Rayleigh scattering is primarily discussed in the context of very small particles compared to wavelengths such as 0.05 μm, and an example that measures up to this scattering region in this explanation collection is the nanotrack. However, since the role of Rayleigh scattering within the fundamental principles is somewhat different, I will limit this to a brief explanation of Rayleigh scattering here. The most common example of Rayleigh scattering is the blue sky. This scattering occurs due to the O2 and N2 molecules surrounding the Earth, resulting in the short-wavelength blue light being enhanced, making the sky appear blue. *For more details, please refer to the related links or feel free to contact us.*

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Scattering of light

Diffraction, refraction, reflection

The fundamental theories of light related to our particle size distribution measuring instrument can be broadly categorized into "scattering," "diffraction," "interference," "refraction and reflection," and "absorption." The particle size distribution measuring devices handled by Nikkiso apply the phenomenon of light scattering to measure the particle size distribution based on the relationship between the intensity of scattered light and the size of the particles. The characteristics of each device will be explained later in the principles section, but here we will first explain the general phenomenon of "scattering." When we talk about light scattering, it often refers to everything other than the light that travels in a straight line when light is directed at a certain substance. In other words, it is the result of a combination of the three phenomena: "diffraction," "refraction," and "reflection." *For more details, please refer to the related links or feel free to contact us.*

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Particle size distribution

To properly evaluate powder particles, not only the average particle size but also the particle size distribution is important.

The size of particles as a bulk, that is, as an aggregate, is typically represented by the distribution of the presence ratio for various measurement results according to size (particle diameter). The criteria for the presence ratio can be based on volume (volume distribution), number (number distribution), etc. In microtrack (laser diffraction and scattering method), volume distribution is measured in principle. (It is easy to convert to number criteria using software, assuming the shape of the particles is spherical.) The sedimentation method is a mass-based measurement method, but since the density of the sample is required during the measurement process, volume distribution can also be obtained. In dynamic light scattering, it is common to obtain the presence ratio as the relative intensity of the signal, but in the case of nanotracks, volume distribution can be output. Particle size distribution can be represented as frequency or as a cumulative distribution. The cumulative distribution can have an oversize curve that rises to the right with fine particles set to zero, and an undersize curve that falls to the right with coarse particles set to zero. *For more details, please refer to the related links or feel free to contact us.*

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