• Aug 25, 2022
• Physical Measurement
• By Rebecca Wolfrom

# An Introduction to Surface Area

Surface area is an important property of solids with many industrial applications. This article will cover what surface area is, what affects it, how it is determined and how does gas adsorption work in the laboratory on a practical level. This article has been adapted from Specifics of Surface Area by Rebecca Lea Wolfrom.

### What factors affect surface area and why is it important?

Envision a perfectly smooth, solid, uniform cube of length, width, and height all 10 meters (see Figure 1).

#### Figure 1: A perfectly smooth, solid, uniform cube with equal length, width, and height.

There are six surfaces: the top, the bottom, and four sides. The area (length × width) of each surface is 2 10m×10m = 100m. So, the total area of all surfaces exposed to the environment is 2 2 100m ×6 = 600m.This is the cube’s surface area (SA). If the cube weighs 100 grams, then the surface area per unit weight, or specific surface area (SSA), is defined as Equitation 1:

Slice the cube in half once in each direction as in Figure 2.

#### Figure 2: Slicing the cube in half once in each direction exposes new surface area.

There are newly exposed surfaces to be considered in the overall surface area: 8 new cubes, 5m × 5m × 5m each. A single cube has a surface area of 150 m2, multiplied by eight cubes gives 1200 m2. Since the weight remains the same, the specific surface area of our material is now 12 m2 /g. Subdividing each of these eight cubes, the resulting specific surface area becomes 24 m2 /g. Nothing about the original material has changed except the size of its units. As the particle size gets smaller, more surface becomes exposed and the specific surface area increases.

Even more influential on overall surface area than particle size is the presence of pores. Imparting our smooth solid cube with a system of worm holes and texture will immediately create far more exposed surface than any simple slicing could. Therefore, a material having pore structure of some degree will have greater, possibly exponentially greater, specific surface area than that same material in solid nonporous form (Figure 3).

#### Figure 3: Particle shape (solid sphere, solid cube, solid polyhedron), particle surface texture (rough solid) and porosity (particle full of intruding pores) all affect surface area.

Surface area affects the dissolution rate of powders like pharmaceuticals. It also governs the adsorption capacity of filters like the charcoal in home water purifiers, and it controls the rate of water uptake like hydration in cement preparation, just to name a few. Each feature is critical to the behavior of the final product, and all depend upon the amount of surface available to a reactant. As a result, pharmaceutical, environmental, mining, catalysis, and many other industries have been evaluating the surface area of their materials for decades.

### How is surface area determined?

Because particle size is relatable to surface area, simple geometry much like the aforementioned cube example can be applied to make estimates. A typical size distribution will show the relative amount of particles present in each of many narrow size ranges, so one may apply an assumption for equivalent shapes and thereby roughly sum up an overall surface quantity.

Some manufacturers include a particle size-derived surface area on their default instrument outputs. However, most common particle size techniques all report size in terms of equivalent spherical diameter (ESD).1 While the ESD reporting style is generally known and accepted due to the complex calculations involved, it cannot be regarded as accurate because the material under analysis is rarely made up of perfectly smooth solid spheres. Such data can only be used for relative comparisons between sample sets of the same material at best. Recall the earlier discussion of how significantly porosity can influence surface area: one source claims a possible underestimate of ≥ 1000 m2 /g by ESD calculations because pores, particle shape, and surface irregularities are disregarded.2 In short, surface area values derived from particle size data should never be used without understanding the assumptions behind the calculation.

How, then, can surface area be determined? The most effective way is by gas adsorption, in which individual molecules of an inert gas lay down on the test material surface and occupy a given amount of space. As more and more molecules lay down under a controlled temperature and pressure, eventually (theoretically) a monolayer forms. Gas molecules perfectly pack together with no open spaces between them in a layer one molecule thick. Using the size of each molecule and the quantity of molecules in place, the area is determined as in Equitation 2:

• Q = the quantity of gas molecules covering the surface
• A = the cross-sectional area of one gas molecule at the designated temperature and pressure
• C = mole and volume-to-weight conversions (if needed)
• W = total weight of sample tested.

ISO 9277:2020(EN) and ISO 15901-2:2022(E)3,4 among others define adsorption as enrichment of the gas molecules at external and accessible internal faces of the solid. Note the spelling: ADsorption means the gas molecules are indeed laying down with essentially no motion, but that they may get up at any time with no change to themselves or the surface. The only push needed to drive them off is some change in their environment like a temperature increase or a pressure decrease. Adsorption is not to be confused with ABsorption, where the gas would actually intrude into the surface causing a chemical change. If the gas being used for surface area determination is ABsorbed by the solid, the theoretical assumptions break down and a different gas should be employed.

As shown in Figure 4, the gas being used for measurement is typically referred to as the adsorptive; it changes name to adsorbate and becomes fluid once it has laid still on the surface of the test material. That material is called the adsorbent. These definitions are established in the ISO documents3, 4.

#### Figure 4: Freely moving adsorptive (gas molecules, dark orange spheres) condenses on the surface of the adsorbent (solid surface, blue) to become adsorbate (light orange spheres.)

How does gas adsorption work in the laboratory on a practical level? Understanding the behavior and treatment of gases is critical. Important properties of a pure gas to be considered are as follows:

• Reactivity. The tendency of the gas to react with other materials. Inert gases are chosen for surface area determinations.
• Saturation Pressure. The saturation pressure P0 (or vapor pressure) of the gas, where liquid and gaseous states coexist in equilibrium, where the gas condenses/liquefies at varying temperatures.
• Molecular attributes. Molecular weight and molecular cross-sectional area of the gas at a range of temperatures.

Because the goal of the technique is to encourage fast-moving gas molecules to slow down and physically attach to a surface due to thermodynamics (i.e., condense) at pressures lower than their saturation pressure, the analysis is done at extremely low temperatures. In this way, one can achieve some measurable condensation for a series of pressures leading up to P0 for the gas. Any pure gas may be used as long as it adsorbs weakly to materials by van der Waals forces—a combination of London dispersion forces and polar or polarizable molecular interactions—and it may be used as long as it will readily desorb by either a small decrease in pressure (under constant temperature) or an increase in temperature (at steady pressure.) Nitrogen is the most popular gas to use, mainly because it is readily available in a very pure state; it is generally nonreactive with other substances; has a strong tendency to condense onto surfaces at the temperature of liquid nitrogen, which is also readily available; and it has a generally accepted value for its molecular cross-sectional area at liquid nitrogen temperature5.

A clean sample in an enclosed nonporous, nonreactive (usually glass) cell, having openings for gas admittance only, is cooled in a liquid nitrogen bath, or other extremely cold liquid such as liquid argon or solid carbon dioxide in acetone. A small known amount of adsorptive gas is admitted to the analytical cell to achieve a predetermined pressure at a fraction of its saturation pressure P0. The quantity of gas adsorbed at that pressure is determined by detecting changes in the environment. More increments of gas are then admitted at steadily increasing pressures up toward saturation. Each pressure point in this routine is termed a Relative Pressure P/P0. These adsorbed quantities plotted against each P/P0 point form a plot called an isotherm, so termed because the experiment was done all at the same (iso) temperature (therm).

Classes of materials like silicas or metal oxides can have similar-looking isotherms if the materials have comparable adsorption tendencies. If a researcher is investigating a brand new material, the literature recommends developing an isotherm using non-porous samples of the material, to avoid complicating variables of porosity6. ISO3 refers to IUPAC, which has compiled and named the six typical isotherm shapes found to date7.

### Surface area testing techniques

The specific surface area of any solid may be determined by first developing a gas adsorption isotherm and then by using the well- established BET method of calculating the area occupied by the adsorbed gas within a specific region shown by the isotherm. PTL can advise on the most appropriate techniques suitable for your needs. We have capabilities for mercury porosimetry and various choices of gas physisorption techniques for BET surface area and porosity determination. Please contact us with any questions.

### References

1. Wolfrom, R.L., “The Language of Particle Size,” GXP Compliance Vol. 15, No. 2, Spring 2011.
2. Lowell, S., Shields, S.E., Thomas, M.A., and Thommes, M., Characterization of Porous Solids and Powders: Surface Area, Pore Size, and Density, 2004.
3. ISO 9277:1995(E), Definition of the Specific Surface Area of Solids by Gas Adsorption using the BET Method, 1995.
4. ISO 15901-2:2006(E), Pore Size Distribution and Porosity of Solid Materials by Mercury Porosimetry and Gas Adsorption – Part 2: Analysis of Mesopores and Macropores by Gas Adsorption, 2006.
5. Quantachrome Instruments Primer Series, Surface Area Determination, www.quantachrome.com.
6. Webb, P.A., and Orr, C., Analytical Methods in Fine Particle Technology, 1997.
7. Langmuir, I. Journal of the American Chemical Society, Vol. 40, p. 1368, 1918.