This document specifies the measurement of the size distribution of particles dispersed in an electrolyte solution using the electrical sensing zone method. This can include biologics such as cells, but also industrial particles such as carbon, cement, ceramic powders, metal powders, pigments and polymer powders. The method measures pulse heights and their relationship to particle volumes or diameters, and is applicable over the range (implementation dependant) from approximately 0,5 μm tο above 1 mm. This document does not address the specific requirements of the measurement of specific materials.

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This document provides guidelines and requirements for the determination of aerosol particle number size distribution by means of the analysis of electrical mobility of aerosol particles. This measurement is usually called "differential electrical mobility analysis for aerosol particles". This analytical method is applicable to particle size measurements ranging from approximately 1 nm to 1 µm. This document does not address the specific instrument design or the specific requirements of particle size distribution measurements for different applications but includes the calculation method of uncertainty. In this document, the complete system for carrying out differential electrical mobility analysis is referred to as DMAS (differential mobility analysing system), while the element within this system that classifies the particles according to their electrical mobility is referred to as DEMC (differential electrical mobility classifier). NOTE This document does not include technical requirements and specifications for the application of DMAS, which are defined in application specific standards or guidelines, e.g. for road vehicle applications (ISO/TC 22), environmental measurements (ISO/TC 146) or nanotechnologies (ISO/TC 229).

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This document specifies a method for the application of small-angle X-ray scattering (SAXS) to the estimation of mean particle sizes in the 1 nm to 100 nm size range. It is applicable in dilute dispersions where the interaction and scattering effects between the particles are negligible. This document describes several data evaluation methods: the Guinier approximation, model-based data fitting, Monte-Carlo?based data fitting, the indirect Fourier transform method and the expectation maximization method. The most appropriate evaluation method is intended to be selected by the analyst and stated clearly in the report. While the Guinier approximation only provides an estimate for the mean particle diameter, the other methods also give insight in the particle size distribution.

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This document describes the specifications for spherical polydisperse particulate reference materials with acceptable uncertainty in particle size distribution and describes protocols for their characterization. One potential use of these reference materials is the reliability test of the laser-diffraction instruments and other particle sizing methods. This document expresses polydispersity and the related uncertainties in size. Small variations in size can imply large variations in cumulative distribution. This document describes the requirements of particulate reference materials, which are intended to be used to test the reliability of various types of particle size measurement apparatus. The requirements for processing, homogeneity and stability assessment as well as for the preparation of certificates, which are not addressed in this document are described in ISO 17034.

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This document provides practical guidance for performing and interpreting measurements using dynamic light scattering (DLS) that goes beyond the treatment of measurement artefacts in ISO 22412:2017. This document is intended to help users with experiments planning, in particular with respect to obtaining the necessary information on the sample and deciding whether DLS is the most appropriate method. It provides information on how to prepare samples in an appropriate way, verify the proper functioning of the instrument and interpret the data correctly, including ways to assess data quality. This document focuses on the practical steps required to obtain DLS results of good quality, rather than on theoretical considerations, and covers not only the measurement of solid particles, but also emulsions and bubbles.

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This document provides guidance on instrument qualification and size distribution measurement of particles in many two-phase systems (e.g. powders, sprays, aerosols, suspensions, emulsions and gas bubbles in liquids) through the analysis of their light-scattering properties. It does not address the specific requirements of particle size measurement of specific materials. This document is applicable to particle sizes ranging from approximately 0,1 µm to 3 mm. With special instrumentation and conditions, the applicable size range can be extended above 3 mm and below 0,1 µm. For spherical and non-spherical particles, a size distribution is reported, where the predicted scattering pattern for the volumetric sum of spherical particles matches the measured scattering pattern. This is because the technique assumes a spherical particle shape in its optical model. For non-spherical particles the resulting particle size distribution is different from that obtained by methods based on other physical principles (e.g. sedimentation, sieving).

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This document describes a calibration and verification method for a light extinction liquid-borne particle counter (LELPC), which is used to measure the size and particle number concentration of particles suspended in liquid. The light extinction method described in this document is based on single particle measurements. The typical size range of particles measured by this method is between 1 µm and 100 µm in particle size. The method is applicable to instruments used for the evaluation of the cleanliness of pharmaceutical products (e.g. injections, water for injections, infusions), as well as the measurement of number and size distribution of particles in various liquids. The following are within the scope of this document: — size setting error; — counting efficiency; — size resolution; — maximum particle number concentration; — sampling flow rate error; — sampling time error; — sampling volume error; — calibration interval; — reporting results from test and calibration.

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This document describes a calibration and verification method for a light scattering liquid-borne particle counter (LSLPC), which is used to measure the size and particle number concentration of particles suspended in liquid. The light scattering method described in this document is based on single particle measurements. The typical size range of particles measured by this method is between 0,1 µm and 10 µm in particle size. The method is applicable to instruments used for the evaluation of the cleanliness of pure water and chemicals, as well as the measurement of number and size distribution of particles in various liquids. The measured particle size using the LSLPC depends on the refractive index of particles and medium; therefore, the measured particle size is equivalent to the calibration particles in pure water. The following are within the scope of this document: — size setting error; — counting efficiency; — size resolution; — false count; — maximum particle number concentration; — sampling flow rate error; — sampling time error; — sampling volume error; — calibration interval; — reporting results from test and calibration.

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This document specifies an in situ method for the determination of the density of solid particles or liquid droplets (herein referred to as "particle") dispersed in liquid continuous phase. The method is based on direct experimental determination of particle velocity in these liquids or media in gravitational or centrifugal fields based on Stokes law. The particle density is calculated from experimentally determined particle velocities in different liquids or media, taking into account their dynamic viscosities and densities, respectively. The approach does not require the knowledge of particle size distribution but assumes that sedimentation relevant characteristics (e.g. volume, shape, agglomeration state) do not change. This document does not consider polydispersity with regard to particle density, i.e. all particles are assumed to be of the same material composition.

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This document addresses the zeta-potential measurement operation for applications such as new product design, optimization of existing products, quality control during processing and/or during usage of the product. It does not provide a complete procedure for zeta-potential measurements. The instructions and key points addressed in this document are considered useful for performing zeta-potential measurements as specified in ISO 13099-1 and ISO 13099-2.

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This document describes a calibration and verification method for a light scattering airborne particle counter (LSAPC), which is used to measure the size distribution and particle number concentration of particles suspended in air. The light scattering method described in this document is based on single particle measurements. The typical size range of particles measured by this method is between 0,1 μm and 10 μm in particle size. Instruments that conform to this document are used for the classification of air cleanliness in cleanrooms and associated controlled environments in accordance with ISO 14644‑1 and ISO 14644‑2, as well as the measurement of number and size distribution of particles in various environments. The following parameters are within the scope of this document: — size setting error; — counting efficiency; — size resolution; — false count; — maximum particle number concentration; — sampling flow rate error; — sampling time error; — response rate; — calibration interval; — reporting results from test and calibration.

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ISO 18747-1:2018 specifies a method for the determination of the density of solid particles or liquid droplets (below referred to generically as "particles") dispersed in a liquid. The method is based on the fact that a particle wholly immersed in fluid experiences buoyancy equal to the weight of the fluid displaced by this particle (Archimedean principle), and if its mass force matches the buoyant force, it stops gravitational or centrifugal settling/creaming and the particle remains suspended. This implies that the density of the particle equals the density of the liquid. In this document, particle density determination is conducted by analysing the direction of the migration movement of particles dispersed in liquids with densities that are lower and higher than particle density. All particles are of the same material composition.

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ISO/TR 14411-1:2017 describes the preparation of polydisperse spherical particles based on a picket fence of quasi-monodisperse reference materials, the characterization of its monodisperse components with acceptable uncertainty and the estimation of the uncertainty of the mixture of these particles. This type of material is normally suitable for all particle characterization methods within the appropriate limits of the techniques. An example of using these reference materials in a reliability calculation for a mass-based cumulative size distribution is provided. ISO/TR 14411-1:2017 itself to the technical specificities of preparation beyond the general requirements for certified and non-certified reference materials as described in ISO Guide 30, ISO Guide 31, ISO Guide 35 and ISO 17034.

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ISO 20998-3:2017 gives guidelines for ultrasonic attenuation spectroscopy methods for determining the size distributions of one or more material phases dispersed in a liquid at high concentrations, where the ultrasonic attenuation spectrum is not a linear function of the particle volume fraction. In this regime, particle-particle interactions are not negligible. ISO 20998-3:2017 is applicable to colloids, dispersions, slurries, and emulsions. The typical particle size for such analysis ranges from 10 nm to 3 mm, although particles outside this range have also been successfully measured. Measurements can be made for concentrations of the dispersed phase ranging from about 5 % by volume to over 50 % by volume, depending on the density contrast between the continuous and the dispersed phases, the particle size, and the frequency range[9] [10]. These ultrasonic methods can be used to monitor dynamic changes in the size distribution, including agglomeration or flocculation.

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ISO 22412:2017 specifies the application of dynamic light scattering (DLS) to the measurement of average hydrodynamic particle size and the measurement of the size distribution of mainly submicrometre-sized particles, emulsions or fine bubbles dispersed in liquids. DLS is also referred to as "quasi-elastic light scattering (QELS)" and "photon correlation spectroscopy (PCS)," although PCS actually is one of the measurement techniques. ISO 22412:2017 is applicable to the measurement of a broad range of dilute and concentrated suspensions. The principle of dynamic light scattering for a concentrated suspension is the same as for a dilute suspension. However, specific requirements for the instrument setup and specification of test sample preparation are required for concentrated suspensions. At high concentrations, particle-particle interactions and multiple light scattering can become dominant and can result in apparent particle sizes that differ between concentrated and dilute suspensions.

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ISO 19430:2016 describes the evaluation of the number?based particle size distribution in liquid dispersions (solid, liquid or gaseous particles suspended in liquids) using the particle tracking analysis method for diffusion velocity measurements.

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ISO 15901-1:2016 describes a method for the evaluation of the pore size distribution and the specific surface area of pores in solids by mercury porosimetry according to the method of Ritter and Drake[1][2]. It is a comparative test, usually destructive due to mercury contamination, in which the volume of mercury penetrating a pore or void is determined as a function of an applied hydrostatic pressure, which can be related to a pore diameter. Practical considerations presently limit the maximum applied absolute pressure to about 400 MPa (60 000 psi) corresponding to a minimum equivalent pore diameter of approximately 4 nm. The maximum diameter is limited for samples having a significant depth due to the difference in hydrostatic head of mercury from the top to the bottom of the sample. For the most purposes, this limit can be regarded as 400 µm. The measurements cover inter-particle and intra-particle porosity. In general, without additional information from other methods it is difficult to distinguish between these porosities where they co-exist. The method is suitable for the study of most porous materials non-wettable by mercury. Samples that amalgamate with mercury, such as certain metals, e.g. gold, aluminium, copper, nickel and silver, can be unsuitable with this technique or can require a preliminary passivation. Under the applied pressure some materials are deformed, compacted or destroyed, whereby open pores may be collapsed and closed pores opened. In some cases it may be possible to apply sample compressibility corrections and useful comparative data may still be obtainable. For these reasons, the mercury porosimetry technique is considered to be comparative.

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ISO 27891:2015 describes methods to determine the detection efficiency of condensation particle counters (CPCs) at particle number concentrations ranging between 1 cm-3 and 105 cm-3, together with the associated measurement uncertainty. In general, the detection efficiency will depend on the particle number concentration, the particle size, and the particle composition. The particle sizes covered by the methods described in this International Standard range from approximately 5 nm to 1 000 nm. The methods can therefore be used both to determine a CPC calibration factor to be applied across the range of larger particle sizes where the detection efficiency is relatively constant (the plateau efficiency), and to characterize the drop in CPC detection efficiency at small particle sizes, near the lower detection limit. These parameters are described in more detail in Annex A. The methods are suitable for CPCs whose inlet flows are between approximately 0,1 l/min and 5 l/min. This International Standard describes a method for estimating the uncertainty of a CPC calibration performed according to this International Standard.

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ISO 13317-4:2014 specifies the method for the determination of particle size distribution by the mass of particles settling under gravity in liquid. This method is based on a direct mass measurement and gives the mass distribution of equivalent spherical particle diameter. Typically, the gravitational liquid sedimentation method applies to samples in the 1 μm to 100 μm size range and where the sedimentation condition for particle Reynolds number less than 0,25 is satisfied.

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ISO 13099-3:2014 describes in general electroacoustic effects that can be defined as high frequency electrokinetic phenomena. Particular attention is given to two methods of measurement of electrophoretic mobility of particles suspended in a liquid at high concentration above 1 % v/v, colloid vibration current (CVI) and electric sonic amplitude (ESA), respectively. Estimation of surface charge and determination of zeta potential can be achieved from measured electrophoretic mobility using proper theoretical models, which are described in detail in ISO 13099‑1.

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ISO 9276-2:2014 provides relevant equations and coherent nomenclatures for the calculation of moments, mean particle sizes and standard deviations from a given particle size distribution. Two notation systems in common use are described. One is the method of moments while the second describes the moment-ratio method. The size distribution may be available as a histogram or as an analytical function. The equivalent diameter of a particle of any shape is taken as the size of that particle. Particle shape factors are not taken into account. Samples of particles measured are intended to be representative of the population of particles. For both notation systems, numerical examples of the calculation of mean particle sizes and standard deviation from histogram data are presented in an annex.

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ISO 13322-1:2014 is applicable to the analysis of images for the purpose of determining particle size distributions where the velocity of the particles against the axis of the optical system of the imaging device is zero. The particles are appropriately dispersed and fixed in the object plane of the instrument. The field of view may sample the object plane dynamically either by moving the sample support or the camera provided this can be accomplished without any motion effects on the image. Captured images can be analysed subsequently. ISO 13322-1:2014 concentrates upon the analysis of digital images created from either light or electron detection systems. It considers only image evaluation methods using complete pixel counts.

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ISO 12154:2014 specifies a method for rapid and efficient determination of the skeleton density of solid material samples of regular or irregular shape, whether powdered or in one piece, by means of a gas displacement pycnometer.

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ISO 20998-2:2013 describes ultrasonic attenuation spectroscopy methods for determining the size distributions of a particulate phase dispersed in a liquid at dilute concentrations, where the ultrasonic attenuation spectrum is a linear function of the particle volume fraction. In this regime, particle?particle interactions are negligible. Colloids, dilute dispersions, and emulsions are within the scope of ISO 20998-2:2013. The typical particle size for such analysis ranges from 10 nm to 3 mm, although particles outside this range have also been successfully measured. For solid particles in suspension, size measurements can be made at concentrations typically ranging from 0,1 % volume fraction up to 5 % volume fraction, depending on the density contrast between the solid and liquid phases, the particle size, and the frequency range. For emulsions, measurements may be made at much higher concentrations. These ultrasonic methods can be used to monitor dynamic changes in the size distribution. While it is possible to determine the particle size distribution from either the attenuation spectrum or the phase velocity spectrum, the use of attenuation data alone is recommended. The relative variation in phase velocity due to changing particle size is small compared to the mean velocity, so it is often difficult to determine the phase velocity with a high degree of accuracy, particularly at ambient temperature. Likewise, the combined use of attenuation and velocity spectra to determine the particle size is not recommended. The presence of measurement errors (i.e. "noise") in the magnitude and phase spectra can increase the ill-posed nature of the problem and reduce the stability of the inversion.

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ISO 26824:2013 establishes a vocabulary of terms and definitions relevant to the particle characterization of particulate systems. It covers such fields as the representation of results of particle size analysis, the descriptive and quantitative representation of particle shape and morphology, sample preparation, specific surface area and porosity characterization and measurement methods including sedimentation, classification, acoustic methods, laser diffraction, dynamic light scattering, single particle light interaction methods, differential electrical mobility analysis and image analysis, in a size scale from nanometre to millimetre.

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ISO/TR 13097:2013 addresses the stability characterization of liquid dispersions (suspensions, emulsions, foams and mixtures thereof) for applications, such as new product design, optimization of existing products, quality control during processing and during usage of the product. The stability of a dispersion in the sense of ISO/TR 13097:2013 is defined in terms of the change in one or more physical properties over a given time period.

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This part of ISO 13099 describes methods of zeta-potential determination, both electric and acoustic, in heterogeneous systems, such as dispersions, emulsions, porous bodies with liquid dispersion medium. There is no restriction on the value of zeta-potential or the mass fraction of the dispersed phase; both diluted and concentrated systems are included. Particle size and pore size is assumed to be on the micrometre scale or smaller, without restriction on particle shape or pore geometry. The characterization of zeta-potential on flat surfaces is discussed separately. The liquid of the dispersion medium can be either aqueous or non-aqueous with any liquid conductivity, electric permittivity or chemical composition. The material of particles can be electrically conducting or non-conducting. Double layers can be either isolated or overlapped with any thickness or other properties. This part of ISO 13099 is restricted to linear effects on electric field strength phenomena. Surface charge is assumed to be homogeneously spread along the interfaces. Effects associated with the soft surface layers containing space distributed surface charge are beyond the scope.

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This part of ISO 13099 specifies two methods of measurement of electrophoretic mobility of particles suspended in a liquid: video microscopy and electrophoretic light-scattering. Estimation of surface charge and determination of zeta-potential can be achieved from measured electrophoretic mobility using proper theoretical models, which are described in detail in ISO 13099-1.

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ISO 9277:2010 specifies the determination of the overall specific external and internal surface area of disperse (e.g. nano-powders) or porous solids by measuring the amount of physically adsorbed gas according to the Brunauer, Emmett and Teller (BET) method. It takes account of the International Union for Pure and Applied Chemistry (IUPAC) recommendations of 1984 and 1994. The BET method is applicable only to adsorption isotherms of type II (disperse, nonporous or macroporous solids) and type IV (mesoporous solids, pore diameter between 2 nm and 50 nm). Inaccessible pores are not detected. The BET method cannot reliably be applied to solids which absorb the measuring gas. A strategy for specific surface area determination of microporous materials (type I isotherms) is described in an annex.

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ISO 21501-1:2009 specifies characteristics of a light scattering aerosol spectrometer (LSAS) which is used for measuring the size, number concentration and number/size distribution of particles suspended in a gas. The light scattering technique described in this document is based upon single particle measurements. The size range of particles measured by this method is between approximately 0,06 µm to 45 µm in diameter. Instruments that conform to ISO 21501-1:2009 are used for the determination of the particle size distribution and particle number concentration at relatively high concentrations of up to 1011 particles/m3. Application fields include: characterization of metered dose inhalers (MDI), dry powder inhalers (DPI) and nebulizers in pharmacy; production control of active agents; cut-off determination: impactors, cyclones and impingers; atmospheric aerosols: bio-aerosols, stables/composting facilities, nebulized droplets, measurements in street tunnels; fractional separation efficiency determination of filters. For the above-mentioned applications, aerosol spectrometers should determine the particle size distribution, particle number concentration, size resolution and sizing accuracy as accurately as possible. These aerosol spectrometers are not suitable for the classification of clean rooms.

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ISO 9276-6:2008 specifies rules and nomenclature for the description and quantitative representation of particle shape and morphology. To achieve a more comprehensive description of a particle or particle system, particle size information can be used together with other information but, in most cases, the particle size information cannot be replaced. The averaging of shape over all particles in a sample has been shown to be an ineffective approach. Distributions of other particle characteristics are required in addition to particle size distributions (see ISO 9276‑1). The relevance, to technological applications, of any method of representing particle shape is the deciding factor in its use. Therefore this part of ISO 9276 is restricted to methods which can be correlated with physical properties in industrial applications. The aim of particle analysis is to determine the most appropriate characterization method for a particular application. This implies a profound understanding of the relationship between particle characteristics and macroscopic product and process properties (or at least a database of broad empirical data). Problems of shape and morphology would normally be three-dimensional problems, but most definitions in this part of ISO 9276 are in fact given for two dimensions because of the widespread use of image analysis methods.

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ISO 9276-3:2008 specifies methods for the adjustment of an experimental curve to a reference model with respect to a statistical background. Furthermore, the evaluation of the residual deviations, after the adjustment, is also specified. The reference model can also serve as a target size distribution for maintaining product quality. ISO 9276-3:2008 specifies procedures that are applicable to the following reference models: a) normal distribution (Laplace-Gauss): powders obtained by precipitation, condensation or natural products (pollens); b) log-normal distribution (Galton MacAlister): powders obtained by grinding or crushing; c) Gates-Gaudin-Schuhmann distribution (bilogarithmic): analysis of the extreme values of the fine particle distributions; d) Rosin-Rammler distribution: analysis of the extreme values of the coarse particle distributions; e) any other model or combination of models, if a non-linear fit method is used. ISO 9276-3:2008 can substantially support product quality assurance or process optimization related to particle size distribution analysis.

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ISO 14488:2007 specifies methods for obtaining a test sample from a defined bulk of particulate material (powder, paste, suspension or dust) that can be considered to be representative of that bulk with a defined confidence level. It is particularly relevant to the measurement of particle size, size distribution and surface area.

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ISO 13318-2:2007 covers methods for determining the particle size distribution of particulate materials by means of centrifugal sedimentation in a liquid. Solids concentrations are determined by the transmission of a light beam. The resulting signal enables conversion to a particle size distribution. The method of determining the particle size distribution described in ISO 13318-2:2007 is applicable to powders that can be dispersed in liquids, powders that are present in slurry form and some emulsions. Typical particle size range for analysis is from about 0,1 µm to 5 µm. The method is applicable to powders in which all particles have the same density and comparable shapes and do not undergo chemical or physical change in the suspension liquid. It is usually necessary that the particles have a density higher than that of the liquid.

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ISO 15901-3:2007 describes methods for the evaluation of the volume of micropores (pores of internal width less than 2 nm) and the specific surface area of microporous material by low-temperature adsorption of gases These are comparative, non-destructive tests. The methods use physisorbing gases that can penetrate into the pores under investigation. The method is applicable to isotherms of type I, II, IV or VI of the IUPAC classification (see ISO 15901-2:--, Figure 1, and ISO 9277). The methods in ISO 15901-3:2007 are not applicable when chemisorption or absorption takes place.

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ISO 15901-2:2006 describes a method for the evaluation of porosity and pore size distribution by gas adsorption. It is a comparative, rather than an absolute test. The method is limited to the determination of the quantity of a gas adsorbed per unit mass of sample at a controlled, constant temperature. ISO 15901-2:2006 does not specify the use of a particular adsorptive gas, however nitrogen is the adsorptive gas most commonly used in such methods. Similarly, the temperature of liquid nitrogen is the analysis temperature most commonly used. Use is sometimes made of other adsorptive gases, including argon, carbon dioxide and krypton, and other analysis temperatures, including those of liquid argon and solid carbon dioxide. In the case of nitrogen adsorption at liquid nitrogen temperature, the basis of this method is to measure the quantity of nitrogen adsorbed at 77 K as a function of its relative pressure. Traditionally, nitrogen adsorption is most appropriate for pores in the approximate range of widths 0,4 nm to 50 nm. Improvements in temperature control and pressure measurement now allow larger pore widths to be evaluated. ISO 15901-2:2006 describes the calculation of mesopore size distribution between 2 nm and 50 nm, and of macropore distribution up to 100 nm. The method described in ISO 15901-2:2006 is suitable for a wide range of porous materials, even though the pore structure of certain materials is sometimes modified by pretreatment or cooling. Two groups of procedures are specified to determine the amount of gas adsorbed: those which depend on the measurement of the amount of gas removed from the gas phase (i.e. gas volumetric methods), and those which involve the measurement of the uptake of the gas by the adsorbent (i.e. direct determination of increase in mass by gravimetric methods). In practice, static or dynamic techniques can be used to determine the amount of gas adsorbed. To derive pore size distribution from the isotherm, it is necessary to apply one or more mathematical models, which entails simplifying certain basic assumptions.

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ISO 13322-2:2006 describes methods for controlling the position of moving particles in a liquid or gas and on a conveyor, as well as the image capture and image analysis of the particles. These methods are used to measure the particle sizes and their distributions, the particles being appropriately dispersed in the liquid or gas medium or on the conveyor. The practical limitations of the derived particle size are addressed when using ISO 13322-2:2006.

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ISO 20998-1:2006 describes ultrasonic methods for determining the size distributions of one or more material phases dispersed in a liquid. Colloids, dispersions, slurries and emulsions are within the scope of ISO 20998-1:2006. The typical particle size for such analysis ranges from 10 nm to 3 mm, although particles outside this range have also been successfully measured. Measurements can be made for concentrations of the dispersed phase ranging from 0,1 % by volume up to 50 % or more by volume, depending on the density contrast between the continuous and the dispersed phases. These methods can be used to monitor dynamic changes in the size distribution, including agglomeration or flocculation in concentrated systems.

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The main objective of ISO 9276-5:2005 is to provide the background for the representation of a cumulative particle size distribution which follows a logarithmic normal probability distribution, as a means by which calculations performed using particle size distribution functions may be unequivocally checked. The design of logarithmic normal probability graph paper is explained, as well as the calculation of moments, median diameters, average diameters, and volume-specific surface area. Logarithmic normal probability distributions are often suitable for the representation of cumulative particle size distributions of any dimensionality. Their particular advantage lies in the fact that cumulative distributions, such as number-, length-, area-, volume- or mass-distributions, are represented by parallel lines, all of whose locations may be determined from a knowledge of the location of any one.

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ISO 13318-3:2004 describes a method for determining the particle size distributions of homogeneous particulate material using centrifugal sedimentation in a liquid. Solids concentrations are determined by the attenuation of an X-ray beam. The resulting signal enables conversion to a particle size distribution. The method of determining the particle size distribution described in this standard is applicable to powders which can be dispersed in liquids or powders which are present in slurry form. The typical particle size range for analysis is from 0,1 m to 5 m. The method is applicable to powders in which all particles have the same effective density, chemical composition and comparable shapes. Materials possessing elements with an atomic number greater than about 12 can be expected to produce adequate X-ray opacity. Particles should not undergo chemical or physical change in the suspension liquid. It is necessary that the particles have a higher density than that of the liquid.

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