The specific surface area of a powder is one of the basic properties of the powder. This value represents the internal and external surface area of total particles contained in a unit mass of powder, which can be measured using various probes, such as gases and liquids. In the case of the adsorption method, adsorptive gas as a probe molecule must be accessible to all of the surfaces in cavities, cracks and micropores. Nowadays, powders used as raw materials and intermediate manufactured goods come to more important materials, and industrial needs concerning particle size, particle shape, purity and uniformity of powders become more severe. When the particle size decreases markedly, powdery phenomena depend largely on surface properties. Therefore, characterization of the powder surface becomes significant more and more with a decrease in the diameter of powder particles.

The surface area of powder is generally determined by the gas adsorption method. In this case, it is necessary to obtain the monolayer capacity and cross-sectional area of an adsorbate molecule. To estimate the monolayer capacity Vm, the Brunauer–Emmett–Teller (BET) has been applied to experimental adsorption data. Usually, it can be classfied as single-point BET and multi-point BET, here is a basic introduction of these two theories.

Single-point BET theory

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 or by volumetric gas adsorption. 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, using the following equation for calculating Vm:

                                              equation 1

The specific surface area is then calculated from the value of Vm by below equation 2.

equation 2

N = Avogadro constant (6.022 × 1023 mol⁻¹),

a = effective cross-sectional area of one adsorbate molecule, in square metres (0.162 nm2 for nitrogen and 0.195 nm2 for krypton), m = mass of test powder, in grams,

22400 = volume occupied by 1 mole of the adsorbate gas at STP allowing for minor departures from the ideal, in millilitres.

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 C is 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 multiple-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 Vm is calculated from the single value of Va measured at a single value of P/Po by the equation 3:

equation 3

The specific surface area is calculated from Vm by equation 2 given above.

By reducing the experimental requirement to only one data point, the single-point method offers the advantages of simplicity and speed often with little loss in accuracy.

Multi-point BET theory

The Brunauer-Emmett-Teller (BET) method is commonly applied to calculate the specific surface area on the basis of nitrogen adsorption isotherm measurements at 77 K. Usually, data in the relative pressure range from 0.05 to 0.3 are used. On all surfaces the BET model fails to accurately predict the multilayer adsorption behavior above P/P0=0.5 (the onset of capillary condensation which fills pores with liquid adsorbate). The BET model assumes multilayer adsorption of gas on the adsorbent’s surface.

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 equation 4.

• Once X_m is  determined, the total surface area S_t can be calculated with the following equation 5, 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.

equation 4

equation 5

The BET determination testing can offer 1 point BET, 3 points BET, 5 points BET, 7 points BET etc. analysis, but what is the difference? The more BET points included in the measurement, the more resolution the instrument has when determining where the monolayer forms. A 1 point BET specific surface area analysis is usually recommended for materials for which we have a very good idea where the monolayer forms. A 3 point or 5 point BET specific surface area analysis is useful when we want a little more confidence in finding where the monolayer forms. But for multi-point BET report, should discard those higher P/P0 values that clearly do not lie on a straight BET line. The upper limit of the linear BET range can usually be obtained by calculating the single-point BET area using each data point in turn. Normally, the calculated single-point area will increase with increasing P/P0 up to some maximum, beyond which the calculated value will decrease. That maximum indicates the upper limit for the multi-point range.

Should be aware that if C is large and X_m is small, the BET equation reduces to the Langmuir equation. In a BET report, the 'C' constant varies from solid to solid. Low values represent weak gas adsorption typical of low surface area solids, organics and metals in particular. The larger is  the value of 'C', the sooner will be maltilayer form and convexity of the isotherm increases toward the low pressure range.

Approximate values of C

• C= 2 to 50, mostly be metals, polymers, organics etc.

• C= 50 to 200, mostly be oxides, silicates etc.

• C=＞200, mostly be activated carbons, zeolites etc.

The difference between single-point and multi-point BET

Single-point BET is just a simplified case of multi-point BET. 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.

Usually, the multi-point BET surface area determination is calculated taking into consideration the whole surface like surface of pores, external surface etc and it is generally more reliable than single point determination which is usually used for quick testing and very often comes with lower values.

Single-point BET is just a simplified case of multi-point BET, the calculation will be faster. Single-point BET is also used for determine the appropriate range of P/P0.

There is no huge difference between both ones, but usually multipoint SA is higher than single point which not exceeds 4% difference. so the single point value is very close to the multi-point value, but typically a bit lower in value. This derives directly from the assumptions that were used to derive the single point equation, in a production environment that difference proves to be completely negligible.

Reference List:

• The LibreTexts libraries

• Researchgate

• M. Jaroniec, A. Sayari, in Studies in Surface Science and Catalysis, 1998

• European pharmacopoeia 6.0

• Particle size measurement Vols 1 &2 by Terence Allen 5th edition

• Particle characterization: light scattering methods by Ren Xu (2000)