Adsorption isotherm--GOLD APP INSTRUMENTS

Adsorption isotherm

Adsorption isotherm is the relationship between the pressure and adsorption amount at a constant temperature. The horizontal axis is the relative pressure (P/P₀) which is the equilibrium pressure divided by the saturation pressure. The relative pressure can be 0 to 1 and P/P₀ =1.0 means that the condensation of adsorptive occurs in the sample cell. So an adsorption isotherm is the measurement of adsorptive density which becomes higher than the than the bulk (gas) phase density due to the interaction between the adsorptive and solid surface atoms below its condensation pressure. Adsorption amount in the vertical axis is commonly expressed as V/ml(STP)g^-1 which is expressed by the standard gas volume (at 0^oC and 1 atm).

The figure indicates the classification of adsorption isotherms defined by IUPAC. The type of adsorption isotherm is determined by the pore size and surface character of the material.

I : Microporous materials (e.g. Zeolite and Activated carbon)

II : Non porous materials (e.g. Nonporous Alumina and Silica)

III : Non porous materials and materials which have the weak interaction between the adsorbate and adsorbent (e.g. Graphite/water)

IV : Mesoporous materials (e.g. Mesoporous Alumina and Silica)

V : Porous materials and materials that have the weak interaction between the adsorbate and adsorbent (e.g. Activated carbon/water)

VI : Homogeneous surface materials (e.g. Graphite/Kr and NaCl/Kr)

 

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A novel method for deriving true density of pharmaceutical solids including hydrates and water-containing powders

True density is commonly measured using helium pycnometry. However, most water-containing powders, for example, hydrates, amorphous drugs and excipients, and most tablet formulations, release water when exposed to a dry helium atmosphere. Because released water brings significant errors to the measured true density and drying alters the nature of water-containing solids, the helium pycnometry is not suitable for those substances. To overcome this problem, a novel method has been developed to accurately calculate powder true density from compaction data. No drying treatment of powder samples is required. Consequently, the true density thus obtained is relevant to tableting characterization studies because no alteration to the solid is induced by drying. This method involves nonlinear regression of compaction pressure-tablet density data based on a modified Heckel equation. When true density values of water-free powders derived by this novel method were plotted against values measured using pycnometry, a regression line with slope close to unity and intercept close to zero was obtained. Thus, the validity of this method was supported. Using this new method, it was further demonstrated that helium pycnometry always overestimates true densities of water containing powders, for example, hydrates, microcrystalline cellulose (MCC), and tablet formulations. The calculated truedensities of powders were the same for different particle shapes and sizes of each material. This further suggests that true density values calculated using this novel method are characteristic of given materials and independent of particulate properties.

 

Copyright 2004 Wiley-Liss, Inc. and the American Pharmacists Association

 

 

 

 

published papers

Surface Area|Pore Size|Pore Volume|Pore Size Distribution|Gas Pycnometer|Helium Density Analyzer|High Pressure Volumetric Analyzer|Powder and Porous Analysing|Laboratory Equipment|Research Instruments-Gold APP Instruments

Gas Pycnometer HeliumTrue Density Equipment|High Pressure Volumetric Analyzer| Langmuir/BET/Gibbs/BJH/MP/SF/DR/DA/HK/T-Plot Analyzer

BET Surface Area|Porosity Analyzer|Gas Pycnometer Helium Abosulte Density Equipment|High Pressure Volumetric Analyzer| Langmuir/BET/Gibbs/BJH/MP/SF/DR/DA/HK/T-Plot Analyzer

Langmuir surface area introduction--GOLD APP INSTRUMENTS

1.      The Langmuir Isotherm

Whenever a gas is in contact with a solid there will be an equilibrium established between the molecules in the gas phase and the corresponding adsorbed species (molecules or atoms) which are bound to the surface of the solid.

As with all chemical equilibria, the position of equilibrium will depend upon a number of factors :

1. The relative stabilities of the adsorbed and gas phase species involved
2. The temperature of the system (both the gas and surface, although these are normally the same)
3. The pressure of the gas above the surface

In general, factors (2) and (3) exert opposite effects on the concentration of adsorbed species - that is to say that the surface coverage may be increased by raising the gas pressure but will be reduced if the surface temperature is raised.

The Langmuir isotherm was developed by Irving Langmuir in 1916 to describe the dependence of the surface coverage of an adsorbed gas on the pressure of the gas above the surface at a fixed temperature. There are many other types of isotherm (Temkin, Freundlich ...) which differ in one or more of the assumptions made in deriving the expression for the surface coverage; in particular, on how they treat the surface coverage dependence of the enthalpy of adsorption. Whilst the Langmuir isotherm is one of the simplest, it still provides a useful insight into the pressure dependence of the extent of surface adsorption.

Important Note - Surface Coverage & the Langmuir Isotherm

When considering adsorption isotherms it is conventional to adopt a definition of surface coverage (θ) which defines the maximum (saturation) surface coverage of a particular adsorbate on a given surface always to be unity, i.e. θ_max = 1 .

This way of defining the surface coverage differs from that usually adopted in surface science where the more common practice is to equate θ with the ratio of adsorbate species to surface substrate atoms (which leads to saturation coverages which are almost invariably less than unity).

2.       Langmuir Isotherm - derivation from equilibrium considerations

We may derive the Langmuir isotherm by treating the adsorption process as we would any other equilibrium process - except in this case the equilibrium is between the gas phase molecules (M), together with vacant surface sites, and the species adsorbed on the surface. Thus, for a non-dissociative (molecular) adsorption process we consider the adsorption to be represented by the following chemical equation :

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What Is Adsorption--GOLD APP INSTRUMENTS

The adsorption study has quite a long history. The first document on adsorption is considered to be the study of adsorption behavior of charcoal by Fontana published in 1777. In 1814, N.T. Saussure did a lot of adsorption experiments onto charcoal. Now, his adsorption apparatus is in the exhibition of National Historical Museum in England. The adsorption technology today is widely used in the industrial process (e.g. gas and vapor separation) and characterization of fine materials.

An example of adsorption is visualizedin the figure. From the figure, it is unclear that how the chemisorptionand physisorption are different. Generally, if theinteraction between the adsorbate and adsorbent is strong (e.g. hydrogenbonding or acid-base adsorption) so that the adsorbate cannot be desorbed byvacuuming at the adsorption temperature or room temperature, it is calledchemisorption. Physisorption, on the other hand, is the weak interaction mainlydue to the van der Waals forces. The adsorbate can be easily desorbed byvacuuming. Recently, instead of using the terms “physisorption” and“chemisorption”, “reversible” and “irreversible” adsorption are also used.

What Is The Difference Between Pore Size and Pore Size Distribution

Whereas pore size is a measure of the diameter of the largest pore, pore size distribution is a measure of the range of pore sizes. The range of pore sizes can be normally distributed, and the spread can be quite narrow (e.g. the ratio of largest to smallest may be less than 2). On the other hand, pore size distribution can be very heterogeneous. In the case of large spreads and heterogeneity, the pore size will be far less predictive of flow rate (either filtration or capillary) than it will be for a membrane with a narrow pore size distribution. It is important to note that the pore size corresponding to the bubble point is not at the middle of the distribution, but is the largest pore.

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Zeilites physical characteristics

Zeolites are microporous, aluminosilicate minerals commonly used as commercial adsorbents. The term zeolite was originally coined in 1756 by Swedish mineralogist Axel Fredrik Cronstedt, who observed that upon rapidly heating the material stilbite, it produced large amounts of steam from water that had been adsorbed by the material. Based on this, he called the material zeolite, from the Greek ζέω (zéō), meaning "to boil" and λίθος (líthos), meaning "stone".As of October 2012, 206 unique zeolite frameworks have been identified, and over 40 naturally occurring zeolite frameworks are known.Zeolites are widely used in industry for water purification, as catalysts, for the preparation of advanced materials and in nuclear reprocessing. They are used to extract nitrogen from air to increase oxygen content for both industrial and medical purposes. Their biggest use is in the production of laundry detergents. They are also used in medicine and in agriculture. 

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Porosity in Natural Soils--by GOLD APP INSTRUMENTS

 The porosity of a soil depends on several factors, including (1) packing density, (2) the breadth of the particlesize distribution (polydisperse vs. monodisperse), (3) the shape of particles, and (4) cementing. Mathematically considering an idealized soil of packed uniform spheres, φ must fall between 0.26 and 0.48, depending on the packing. Spheres randomly thrown together will have φ near the middle of this range, typically 0.30 to 0.35. A sand with grains nearly uniform in size (monodisperse) packs to about the same porosity as spheres. In a polydisperse sand, the fit-ting of small grains within the pores between large ones can reduce φ, conceivably below the 0.26 uniform-sphere minimum. Figure 2 illustrates this concept. The particular sort of arrangement required to reduce φ to 0.26 or less is highly improbable, however, so φ also typically falls within the 0.30-0.35 for polydisperse sands. Particles more irregular in shape tend to have larger gaps between their nontouching surfaces, thus forming media of greater porosity. In porous rock such as sand-stone, cementation or welding of particles not only creates pores that are different in shape from those of particulate media, but also reduces the porosity as solid material takes up space that would otherwise be pore space. Porosity in such a case can easily be less than 0.3, even approaching 0. Cementing material can also have the opposite effect. In many soils, clay and organic substances cement particles together into aggregates. An individual aggregate might have a 0.35 porosity within it, but the medium as a whole has additional pore space in the form of gaps between aggregates, so that φ can be 0.5 or greater. Observed porosities can be as great as 0.8 to 0.9 in a peat (extremely high organic matter) soil.

Porosity is often conceptually partitioned into two components, most commonly called textural and structural porosity. The textural component is the value the porosity would have if the arrangement of the particles were random, as described above for granular material without cementing. That is, the textural porosity might be about 0.3 in a granular medium. The structural component represents nonrandom structural influences, including macropores and is arithmetically defined as the difference between the textural porosity and the total porosity.

The texture of the medium relates in a general way to the pore-size distribution, as large particles give rise to large pores between them, and therefore is a major influence on the soil water retention curve. Additionally, the structure of the medium, especially the pervasive-ness of aggregation, shrinkage cracks, worm-holes, etc. substantially influences water retention.

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V-Sorb 4800P surface area and particle size analyzer

Microporo analysis--by GOLD APP INSTRUMENTS

There are t-plot, HK, SF, DR-plot, NLDFT and GCMC method for the evaluation of micropore. t-plot and DR-plot are used to determine the pore volume and separation of internal and external surface area of the particle. HK, SF, NLDFT and GCMC method are used to determine the pore size distribution.

Since the micropore analysis theories must describe the short-range interaction of adsorbate and pore wall, it is not as easy as describing the flat surface adsorption or mesopore adsorption. The typical assumption of these theories is that the pore shape is a slit or cylinder. As the parameters, the surface atoms of pore wall and adsorbate molecules must be selected (e.g. oxygen/carbon, N₂/Ar). If the sample has uniform and homogeneous pores, the calculated pore size will be accurate. However, most of real materials have nonuniform and heterogeneous pores which are not fit to the assumption of the theories. This disagreement is true not only for the pore size distribution obtained from the gas adsorption but also for other porosimetry and particle size measurement. The gas adsorption so far is the best method for the evaluation of micropores compared to other methods because the probe gas molecule size is below nm to detect micropores.

Our recommend method of micropore analysis is as follows: For zeolitic materials, measure them with the Ar adsorption isotherm at 87K and analyze by the cylindrical pore model theory (SF, NLDFT, and GCMC). N₂ molecules, which have strong quadrupole moment, strongly attract to the cation sites and OH group on the surface. For activated carbon materials, they are often measured with N₂ adsorption isotherm at 77K and analyzed by the slit pore model theory (HK, NLDFT, and GCMC).

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Method of pore size distribution measurement--by GOLD APP INSTRUMENTS

The typical methods to measure the pore size distribution of power and materials are the gas adsorption and mercury porosimetry.

The pore size distribution from the gas adsorption method is commonly analyzed from the nitrogen or Ar adsorption isotherm at their boiling temperature, and it is possible to evaluate the pore size from the molecular size to a few hundred nm. The realistic largest detectable pore size is just over 100nm due to the restriction from the pressure sensor accuracy and temperature stability of coolant. Mercury porosimetry calculates the pore size distribution by pressurizing mercury, which is non-wetting, and measure the corresponding intrusion amount. By this method, it is possible to detect the pore size from a few nm to 1000μm within a short period of time. For the pore size measurement below 10nm, it requires over 140MPa of pressure for the intrusion of mercury, so it is necessary to make sure that the material has the strength to withstand the pressure. Also, by this method, it evaluates the pore size of inkbottle neck (the smallest diameter of the pore) from the principle. The realistic measurement range is from a few 10 nm.

Recently, there are bubble point method and gas permeation method to measure the through pore size of filters and separation membranes.

Determination of pore size distribution

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V-Sorb 2800 Instroduction

Gas porosity--by Gold APP Instruments

Gas porosity is the fraction of a rock or sediment filled with a gas.

Determining the true porosity of a gas filled formation has always been a problem in the oil industry. While natural gas is a hydrocarbon, similar to oil, the physical properties of the fluids are very different, making it very hard to correctly quantify the total amount of gas in a formation. Well logging interpretation of the amount of hydrocarbon in the pore space of a formation, relies on the fluid being oil. Gas is light compared to oil causing density logging (gamma ray emitting sensors) based measurements to produce anomalous signals. Similarly, measurements that rely on detecting hydrogen (neutron emitting sensors) can miss detecting or correctly interpreting the presence of gas because of the lower hydrogen concentration in gas, compared to oil.

By properly combining the two erroneous answers from density and neutron logging, it is possible to arrive at a more accurate porosity than would be possible by interpreting each of the measurements separately.

A popular method of obtaining a formation porosity estimate is based on the simultaneous use of neutron and density logs. Under normal logging conditions, the porosity estimates obtained from these tools agree, when plotted on an appropriate lithology and fluid scale. However, in the case of a reservoir where there is gas instead of water or oil in the pore space, the two porosity logs separate, to form what is referred to as gas crossover. Under these conditions, the true formation porosity lies between the measured neutron and density values. Log interpreters often find it difficult to accurately estimate the true formation porosity from these two curves.

Neutron and density logging tools have different responses to the presence of gas in the formation because of differences in the physics of the measurements. A neutron tool response is sensitive mainly to the number of hydrogen atoms in the formation. During the calibration process, water-filled formations are used to develop porosity algorithms, and under these conditions, a lower number of hydrogen atoms is equivalent to a lower porosity. Consequently, when a gas-filled formation is logged, which has a lower number of hydrogen atoms than a water-filled formation of the same porosity, the porosity estimate will be lower than the true porosity.

The density tool, on the other hand, measures the total number of formation electrons. Like the neutron tool, water-filled formations are used in its calibration process. Under these conditions, a lower number of electrons is equivalent to a lower formation density, or a higher formation porosity. Therefore, logging a gas-filled formation, results in a porosity estimate that is higher than the true porosity. Overlaying the neutron and density curves in a gas-bearing zone results in the classic crossover separation.

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Density Definition and classification

Density: 

One of the most common density measurements involves the determination of the geometric space occupied within the envelope of a solid material... including any interior voids, cracks or pores. This is called geometric, envelope or bulk density and only equals true density when there are no internal openings in the material being measured. 

  Absolute Density:

      1) The ratio of the mass of a volume of solid material to the same volume of water.
2) The mass per unit volume of a solid material expressed in grams per cubic centimeter.

·         Apparent Density: 

       The weight of a unit volume of powder, usually expressed as grams per cubic centimeter, determined by a specific method

·         Bulk Density: Powder in a container or bin expressed in mass unit per volume

·         Density Ratio: 

      The ratio of the determined density of a compact to the absolute density of metal of the same composition, usually expressed as a percentage. Also referred to as a percent theoretical density

·         Dry Density: The mass per unit volume of an unimpregnated sintered part

·         Green Density: The density of a green compact

·         Packed Density: Please see preferred term of tap density

·         Tap Density: 

       The density of a powder when the volume receptacle is tapped or vibrated under specified conditions while being loaded. Each particle of a solid material has the same true density after grinding, milling or processing, but more geometric space is occupied by the material. In other words, the geometric density is less... approaching 50% less than true density if the particles are spherical. Handling or vibration of powdered material causes the smaller particles to work their way into the spaces between the larger particles. The geometric space occupied by the powder decreases and its density increases. Ultimately no further natural particle packing can be measured without the addition of pressure. Maximum particle packing is achieved. Under controlled conditions of tap rate, tap force (fall) and cylinder diameter, the condition of maximum packing efficiency is highly reproducible. This tap density measurement is formalized in the British Pharmacopoeia method for Apparent Volume, ISO 787/11 and ASTM standard test methods B527, D1464 and D4781 for tap density.

·         True Density (true density analyzer G-DenPyc 2900) 

      The true density of powders often differs from that of the bulk material because the process of comminution, or grinding will change the crystal structure near the surface of each particle and therefore the density of each particle in a powder. In addition, voids at the surface of a particle, into which liquids will not penetrate, can generate apparent volume which will cause serious errors when density is measured by liquid displacement. The pycnometer G-DenPyc2900 from Gold APP Instruments are specifically designed to measure the true volume of solid materials by employing Archimedes' principle of fluid (gas) displacement and the technique of gas expansion. True densities are measured using helium gas since it will penetrate every surface flaw down to about one Angstrom, thereby enabling the measurement of powder volumes with great accuracy. The measurement of density by helium displacement often can reveal the presence of impurities and occluded pores which cannot be determined by any other method.

·         Wet Density: The mass per unit of volume of a sintered part impregnated with oil or other nonmetallic material