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Introduction to BET (Brunauer, Emmett and Teller)

By BET (Brunauer, Emmett and Teller) the specific surface area of a sample is measured – including the pore size distribution. This information is used to predict the dissolution rate, as this rate is proportional to the specific surface area. Thus, the surface area can be used to predict bioavailability. Further it is useful in evaluation of product performance and manufacturing consistency.

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The specific surface determined by BET relates to the total surface area (reactive surface) as all porous structures adsorb the small gas molecules. The surface area determined by BET is thus normally larger than the surface area determined by air permeability. The method used complies with Ph. Eu.2.9.26 Method II.

Instrument and measuring principle, BET 

The BET instrument applied by Particle Analytical (Micromeritics Gemini 2375 and Gemini V) determines the specific surface area (m²/g) of pharmaceutical samples. The samples are dried with nitrogen purging or in a vacuum applying elevated temperatures. Unless otherwise instructed we use P/P0  of 0,1, 0,2 and 0,3 as standard measurement points. The volume of gas adsorbed to the surface of the particles is measured at the boiling point of nitrogen (-196°C). The amount of adsorbed gas is correlated to the total surface area of the particles including pores in the surface. The calculation is based on the BET theory. Traditionally nitrogen is used as adsorbate gas. Gas adsorption also enables the determination of size and volume distribution of micropores (0.35 – 2.0 nm)..

BET theory

The specific surface area of a powder is determined by physical adsorption of a gas on the surface of the solid and by calculating the amount of adsorbate gas corresponding to a monomolecular layer on the surface. Physical adsorption results from relatively weak forces (van der Waals forces) between the adsorbate gas molecules and the adsorbent surface area of the test powder. The determination is usually carried out at the temperature of liquid nitrogen. The amount of gas adsorbed can be measured by a volumetric or continuous flow procedure.

Multi-point measurements

The data are treated according to the Brunauer, Emmett and Teller (BET) adsorption isotherm equation:

A value of Va is measured at each of not less than 3 values of P/Po. Then the BET value:

is plotted against P/P_o according to equation (1). This plot should yield a straight line usually in the approximate relative pressure range 0.05 to 0.3. The data are considered acceptable if the correlation coefficient, r, of the linear regression is not less than 0.9975; that is, r² is not less than 0.995. From the resulting linear plot, the slope, which is equal to (C − 1)/V_mC, and the intercept, which is equal to 1/V_mC, are evaluated by linear regression analysis. From these values, V_m is calculated as 1/(slope + intercept), while Cis calculated as (slope/intercept) + 1. From the value of V_m so determined, the specific surface area, S, in m²·g^–1, is calculated by the equation:

A minimum of 3 data points is required. Additional measurements may be carried out, especially when non-linearity is obtained at a P/Po value close to 0.3. Because non-linearity is often obtained at a P/Po value below 0.05, values in this region are not recommended. The test for linearity, the treatment of the data, and the calculation of the specific surface area of the sample are described above.

Single point measurement

Normally, at least 3 measurements of Va each at different values of P/Po are required for the determination of specific surface area by the dynamic flow gas adsorption technique (Method I) or by volumetric gas adsorption (Method II). However, under certain circumstances described below, it may be acceptable to determine the specific surface area of a powder from a single value of Va measured at a single value of P/Po such as 0.300 (corresponding to 0.300 mole of nitrogen or 0.001038 mole fraction of krypton), using the following equation for calculating Vm:

The specific surface area is then calculated from the value of V_m by equation (2) given above.

The single-point method may be employed directly for a series of powder samples of a given material for which the material constant C is much greater than unity. These circumstances may be verified by comparing values of specific surface area determined by the single-point method with that determined by the multiple-point method for the series of powder samples. Close similarity between the single-point values and multiple-point values suggests that 1/C approaches zero.

The single-point method may be employed indirectly for a series of very similar powder samples of a given material for which the material constant Cis not infinite but may be assumed to be invariant. Under these circumstances, the error associated with the single-point method can be reduced or eliminated by using the multi-point method to evaluate C for one of the samples of the series from the BET plot, from which C is calculated as (1 + slope/intercept). Then V_m is calculated from the single value of V_a measured at a single value of P/P_o by the equation:

The specific surface area is calculated from V_m by equation (2) given above.

The following section describes the methods to be used for the sample preparation, the dynamic flow gas adsorption technique (Method I) and the volumetric gas adsorption technique (Method II).

Sample preparation: Outgassing: Before the specific surface area of the sample can be determined, it is necessary to remove gases and vapours that may have become physically adsorbed onto the surface after manufacture and during treatment, handling and storage. If outgassing is not achieved, the specific surface area may be reduced or may be variable because an intermediate area of the surface is covered with molecules of the previously adsorbed gases or vapours. The outgassing conditions are critical for obtaining the required precision and accuracy of specific surface area measurements on pharmaceuticals because of the sensitivity of the surface of the materials.

Conditions: The outgassing conditions must be demonstrated to yield reproducible BET plots, a constant weight of test powder, and no detectable physical or chemical changes in the test powder. The outgassing conditions defined by the temperature, pressure and time should be chosen so that the original surface of the solid is reproduced as closely as possible. Outgassing of many substances is often achieved by applying a vacuum, by purging the sample in a flowing stream of a non-reactive, dry gas, or by applying a desorption-adsorption cycling method. In either case, elevated temperatures are sometimes applied to increase the rate at which the contaminants leave the surface. Caution should be exercised when outgassing powder samples using elevated temperatures to avoid affecting the nature of the surface and the integrity of the sample.

If heating is employed, the recommended temperature and time of outgassing are as low as possible to achieve reproducible measurement of specific surface area in an acceptable time. For outgassing sensitive samples, other outgassing methods such as the desorption-adsorption cycling method may be employed.

The volumetric method (Ph. Eu.2.9.26 Method II)

Principle: In the volumetric method (see Figure 2.9.26.-2), the recommended adsorbate gas is nitrogen which is admitted into the evacuated space above the previously outgassed powder sample to give a defined equilibrium pressure, P, of the gas. The use of a diluent gas, such as helium, is therefore unnecessary, although helium may be employed for other purposes, such as to measure the dead volume.

Since only pure adsorbate gas, instead of a gas mixture, is employed, interfering effects of thermal diffusion are avoided in this method.

Procedure: Admit a small amount of dry nitrogen into the sample tube to prevent contamination of the clean surface, remove the sample tube, insert the stopper, and weigh it. Calculate the weight of the sample. Attach the sample tube to the volumetric apparatus. Cautiously evacuate the sample down to the specified pressure (e.g. between 2 Pa and 10 Pa). Alternatively, some instruments operate by evacuating to a defined rate of pressure change (e.g. less than 13 Pa/30 s) and holding for a defined period of time before commencing the next step.

If the principle of operation of the instrument requires the determination of the dead volume in the sample tube, for example, by the admission of a non-adsorbed gas, such as helium, this procedure is carried out at this point, followed by evacuation of the sample. The determination of dead volume may be avoided using difference measurements, that is, by means of reference and sample tubes connected by a differential transducer. The adsorption of nitrogen gas is then measured as described below.

Raise a Dewar vessel containing liquid nitrogen at 77.4 K up to a defined point on the sample cell. Admit a sufficient volume of adsorbate gas to give the lowest desired relative pressure. Measure the volume adsorbed, V_a. For multi-point measurements, repeat the measurement of V_a at successively higher P/P_o values. When nitrogen is used as the adsorbate gas, P/P_o values of 0.10, 0.20, and 0.30 are often suitable.

Reference materials: Periodically verify the functioning of the apparatus using appropriate reference materials of known surface area, such as α-alumina, which should have a specific surface area similar to that of the sample to be examined.

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Introduction

In the past few years, nanotechnology research has expanded out of the chemistry department and into the fields of medicine, energy, aerospace and even computing and information technology. With bulk materials, the surface area to volume is insignificant in relation to the number of atoms in the bulk, however when the particles are only 1 to 100 nm across, different properties begin to arise. For example, commercial grade zinc oxide has a surface area range of 2.5 to 12 m²/g while nanoparticle zinc oxide can have surface areas as high as 54 m²/g . The nanoparticles have superior UV blocking properties when compared to the bulk material, making them useful in applications such as sunscreen. Many useful properties of nanoparticles rise from their small size, making it very important to be able to determine their surface area.

Overview of BET Theory

The BET theory was developed by Stephen Brunauer (Figure 2.3.12.3.1 ), Paul Emmett (Figure 2.3.22.3.2 ), and Edward Teller (Figure 2.3.32.3.3 ) in 1938. The first letter of each publisher’s surname was taken to name this theory. The BET theory was an extension of the Langmuir theory, developed by Irving Langmuir (Figure 2.3.42.3.4 ) in 1916.

The Langmuir theory relates the monolayer adsorption of gas molecules (Figure 2.3.52.3.5 ), also called adsorbates, onto a solid surface to the gas pressure of a medium above the solid surface at a fixed temperature to 2.3.12.3.1 , where θ is the fractional cover of the surface, P is the gas pressure and α is a constant.Θ = α⋅P1 + (α⋅P)(2.3.1)(2.3.1)Θ = α⋅P1 + (α⋅P)

The Langmuir theory is based on the following assumptions:

• All surface sites have the same adsorption energy for the adsorbate, which is usually argon, krypton or nitrogen gas. The surface site is defined as the area on the sample where one molecule can adsorb onto.
• Adsorption of the solvent at one site occurs independently of adsorption at neighboring sites.
• Activity of adsorbate is directly proportional to its concentration.
• Adsorbates form a monolayer.
• Each active site can be occupied only by one particle.

The Langmuir theory has a few flaws that are addressed by the BET theory. The BET theory extends the Langmuir theory to multilayer adsorption (Figure 2.3.12.3.1 ) with three additional assumptions:

• Gas molecules will physically adsorb on a solid in layers infinitely.
• The different adsorption layers do not interact.
• The theory can be applied to each layer.

How does BET Work?

Adsorption is defined as the adhesion of atoms or molecules of gas to a surface. It should be noted that adsorption is not confused with absorption, in which a fluid permeates a liquid or solid. The amount of gas adsorbed depends on the exposed surface are but also on the temperature, gas pressure and strength of interaction between the gas and solid. In BET surface area analysis, nitrogen is usually used because of its availability in high purity and its strong interaction with most solids. Because the interaction between gaseous and solid phases is usually weak, the surface is cooled using liquid N₂ to obtain detectable amounts of adsorption. Known amounts of nitrogen gas are then released stepwise into the sample cell. Relative pressures less than atmospheric pressure is achieved by creating conditions of partial vacuum. After the saturation pressure, no more adsorption occurs regardless of any further increase in pressure. Highly precise and accurate pressure transducers monitor the pressure changes due to the adsorption process. After the adsorption layers are formed, the sample is removed from the nitrogen atmosphere and heated to cause the adsorbed nitrogen to be released from the material and quantified. The data collected is displayed in the form of a BET isotherm, which plots the amount of gas adsorbed as a function of the relative pressure. There are five types of adsorption isotherms possible.

Type I Isotherm

Type I is a pseudo-Langmuir isotherm because it depicts monolayer adsorption (Figure 2.3.62.3.6 ). A type I isotherm is obtained when P/P_o < 1 and c > 1 in the BET equation, where P/P_o is the partial pressure value and c is the BET constant, which is related to the adsorption energy of the first monolayer and varies from solid to solid. The characterization of microporous materials, those with pore diameters less than 2 nm, gives this type of isotherm.

Type II Isotherm

A type II isotherm (Figure 2.3.72.3.7 ) is very different than the Langmuir model. The flatter region in the middle represents the formation of a monolayer. A type II isotherm is obtained when c > 1 in the BET equation. This is the most common isotherm obtained when using the BET technique. At very low pressures, the micropores fill with nitrogen gas. At the knee, monolayer formation is beginning and multilayer formation occurs at medium pressure. At the higher pressures, capillary condensation occurs.

Type III Isotherm

A type III isotherm (Figure 2.3.82.3.8 ) is obtained when the c < 1 and shows the formation of a multilayer. Because there is no asymptote in the curve, no monolayer is formed and BET is not applicable.

Type IV Isotherm

Type IV isotherms (Figure 2.3.92.3.9 ) occur when capillary condensation occurs. Gases condense in the tiny capillary pores of the solid at pressures below the saturation pressure of the gas. At the lower pressure regions, it shows the formation of a monolayer followed by a formation of multilayers. BET surface area characterization of mesoporous materials, which are materials with pore diameters between 2 – 50 nm, gives this type of isotherm.

Type V Isotherm

Type V isotherms (Figure 2.3.102.3.10 ) are very similar to type IV isotherms and are not applicable to BET.

Calculations

The BET Equation, 2.3.22.3.2 , uses the information from the isotherm to determine the surface area of the sample, where X is the weight of nitrogen adsorbed at a given relative pressure (P/Po), X_m is monolayer capacity, which is the volume of gas adsorbed at standard temperature and pressure (STP), and C is constant. STP is defined as 273 K and 1 atm.1X[(P0/P)−1]=1XmC+C−1XmC(PP0)(2.3.2)(2.3.2)1X[(P0/P)−1]=1XmC+C−1XmC(PP0)

Multi-point BET

Ideally five data points, with a minimum of three data points, in the P/P₀ range 0.025 to 0.30 should be used to successfully determine the surface area using the BET equation. At relative pressures higher than 0.5, there is the onset of capillary condensation, and at relative pressures that are too low, only monolayer formation is occurring. When the BET equation is plotted, the graph should be of linear with a positive slope. If such a graph is not obtained, then the BET method was insufficient in obtaining the surface area.

• The slope and y-intercept can be obtained using least squares regression.
• The monolayer capacity X_m can be calculated with 2.3.32.3.3 .
• Once X_m is determined, the total surface area S_t can be calculated with the following equation, where L_av is Avogadro’s number, A_m is the cross sectional area of the adsorbate and equals 0.162 nm² for an absorbed nitrogen molecule, and M_v is the molar volume and equals 22414 mL, 2.3.42.3.4 .

Xm =1s + i=C−1Cs(2.3.3)(2.3.3)Xm =1s + i=C−1CsS =XmLavAmMv(2.3.4)(2.3.4)S =XmLavAmMv

Single point BET can also be used by setting the intercept to 0 and ignoring the value of C. The data point at the relative pressure of 0.3 will match up the best with a multipoint BET. Single point BET can be used over the more accurate multipoint BET to determine the appropriate relative pressure range for multi-point BET.

Sample Preparation and Experimental Setup

Prior to any measurement the sample must be degassed to remove water and other contaminants before the surface area can be accurately measured. Samples are degassed in a vacuum at high temperatures. The highest temperature possible that will not damage the sample’s structure is usually chosen in order to shorten the degassing time. IUPAC recommends that samples be degassed for at least 16 hours to ensure that unwanted vapors and gases are removed from the surface of the sample. Generally, samples that can withstand higher temperatures without structural changes have smaller degassing times. A minimum of 0.5 g of sample is required for the BET to successfully determine the surface area.

Samples are placed in glass cells to be degassed and analyzed by the BET machine. Glass rods are placed within the cell to minimize the dead space in the cell. Sample cells typically come in sizes of 6, 9 and 12 mm and come in different shapes. 6 mm cells are usually used for fine powders, 9 mm cells for larger particles and small pellets and 12 mm are used for large pieces that cannot be further reduced. The cells are placed into heating mantles and connected to the outgas port of the machine.

After the sample is degassed, the cell is moved to the analysis port (Figure 2.3.112.3.11 ). Dewars of liquid nitrogen are used to cool the sample and maintain it at a constant temperature. A low temperature must be maintained so that the interaction between the gas molecules and the surface of the sample will be strong enough for measurable amounts of adsorption to occur. The adsorbate, nitrogen gas in this case, is injected into the sample cell with a calibrated piston. The dead volume in the sample cell must be calibrated before and after each measurement. To do that, helium gas is used for a blank run, because helium does not adsorb onto the sample.

Shortcomings of BET

The BET technique has some disadvantages when compared to NMR, which can also be used to measure the surface area of nanoparticles. BET measurements can only be used to determine the surface area of dry powders. This technique requires a lot of time for the adsorption of gas molecules to occur. A lot of manual preparation is required.

The Surface Area Determination of Metal-Organic Frameworks

The BET technique was used to determine the surface areas of metal-organic frameworks (MOFs), which are crystalline compounds of metal ions coordinated to organic molecules. Possible applications of MOFs, which are porous, include gas purification and catalysis. An isoreticular MOF (IRMOF) with the chemical formula Zn₄O(pyrene-1,2-dicarboxylate)₃ (Figure 2.3.122.3.12 ) was used as an example to see if BET could accurately determine the surface area of microporous materials. The predicted surface area was calculated directly from the geometry of the crystals and agreed with the data obtained from the BET isotherms. Data was collected at a constant temperature of 77 K and a type II isotherm (Figure 2.3.132.3.13 ) was obtained.

The isotherm data obtained from partial pressure range of 0.05 to 0.3 is plugged into the BET equation, 2.3.22.3.2 , to obtain the BET plot (Figure 2.3.142.3.14 ).

Using 2.3.52.3.5 , the monolayer capactiy is determined to be 391.2 cm³/g.Xm =1(2.66E − 3) + (−5.212E − 0.05)(2.3.5)(2.3.5)Xm =1(2.66E − 3) + (−5.212E − 0.05)

Now that X_m is known, then 2.3.62.3.6 can be used to determine that the surface area is 1702.3 m²/g.S =391.2cm2∗0.162nm2∗6.02∗102322.414:L(2.3.6)(2.3.6)S =391.2cm2∗0.162nm2∗6.02∗102322.414:L