# Krypton surface area and water sorption for common pharmaceutical excipients

The GAB (Guggenheim, Anderson, and de Boer) equation [1, 2, 3] is a widely referenced model that is often used for the characterization of pharmaceuticals, excipients, and food [4, 5, 6, 7].   Three excipients: lactose, gelatin, and talc were characterized in a single sorption instrument using krypton adsorption and BET modeling to determine the as-received surface area, water sorption, and then krypton sorption to determine the impact of water sorption on the BET surface area.  Unlike the BET equation which is usually applied to nitrogen adsorption isotherms and a narrow range of data ($$0.05 < p/p^\circ < 0.30$$), the GAB equation may be applied to water adsorption isotherms and is used to fit a wide range of data ($$0.05 < a_\circ < 0.90$$) [8].

The term activity is used for water sorption studies rather than relative pressure and therefore $$a_\circ = p/p^\circ$$. This convention is retained for the water adsorption isotherms to remain consistent with the application and previously published articles.

Figure 1: Water adsorption isotherms measured at room temperature for gelatin, lactose, and talc.

## Experimental

Three commercially available excipients from Spectrum: gelatin, lactose, and talc were used in this study. Each sample was prepared by simple degassing in vacuo at room temperature overnight (18 hours). The samples were not heated to avoid morphological changes.

After degassing, krypton adsorption isotherms were measured using the Micromeritics 3Flex Surface Characterization Analyzer. The Kr adsorption isotherms were used to determine the surface area of each excipient and the measurements were performed in a parallel hi-speed mode.

Upon completion of the krypton adsorption measurements, the samples were re-degassed using the previously described technique. Upon completion of the preparation, water adsorp- tion isotherms were collected for each excipient also using the Micromeritics 3Flex analyzer. Similar to the krypton analysis, the water adsorption isotherms were collected in a parallel manner and the adsorption isotherms are given in Figure 1.

The excipients were then re-degassed and krypton adsorption was used to determine the surface area of the excipients after exposure to water.

Table 1: Summary of BET surface area results (1 and 3) from krypton sorption isotherms and GAB and BET parameters derived from water adsorption isotherms (2). The BET surface area was determined using krypton adsorption for the as-received excipients (1) and after collecting the water adsorption isotherms (3).
AnalysisBETGABBETBET
Surface AreaPore volumenmCknmCSurface Area
m2/gml/gmg/gmg/gm2/g
Gelatin0.120.194104.915.60.65366.316.30.096
Lactose0.530.0032.0907.50.1991.8148.30.51
Talc7.580.0051.1 82.70.7941.066.17.58

## Data analysis

MicroActive software for the 3Flex analyzer was used for the krypton and water adsorption isotherms. The krypton adsorption data were used to calculate BET surface area for the as-received excipients and the post-water sorption samples. The BET surface areas were calculated using isotherm data over the range of 0.05 – 0.15 relative pressure ($$p/p^\circ$$), Table 1.

### GAB Equation

$$\Large\frac{v}{v_m} = \frac{kCa_o}{(1-ka_o)(1 – ka_o(1-C))}$$

### BET Equation

$$\Large\frac{v}{v_m} = \frac{Ca_o}{(1-a_o)(1 + a_o(C-1))}$$

Water adsorption isotherms were analyzed using both the BET and GAB equations to determine monolayer capacities for water. The MicroActive software features advanced reporting capabilities using the Python programming language. Two simple python scripts were used to aid the analysis of the water adsorption isotherms. The first script that was developed converted the quantity adsorbed (mmoles/g of sample) to mg/g of sample. This is a trivial calculation, however it is a convenience that provides reporting flexibility and allows for users to compare high quality isotherm data with results obtained from micro balances.

A second python script was employed to calculate the GAB parameters for each excipient. The MicroActive software and the use of Python scripting provides user flexibility to add advanced reporting options and make these calculations part of their standard reporting practices.

The GAB and BET parameters for the water adsorption isotherms are listed in table 1. The results from the krypton adsorption analyses indicate the BET surface area of gelatin was reduced 20%, lactose was reduced 4%, and the talc was unchanged after exposure to water.

Figure 2: GAB model (line) for water adsorption isotherms for Gelatin, Lactose, and Talc.

The parameters calculated from the water adsorption isotherms are consistent with previous reports comparing the GAB and BET equations. For all three excipients the monolayer capacity calculated using the GAB equation exceeded the values obtained from the BET equation. It is interesting to note that the BET model was applied to the activity ranging from 0.05 – 0.3 while the GAB equation was used to model the activity over a broader range from 0.05 – 0.8, Figure 2.

## Summary

The Micromeritics 3Flex adsorption analyzer provides a characterization platform for mea- suring the adsorption isotherms of a wide variety of probe molecules. In this study, we have used krypton to accurately determine the surface area of pharmaceutical excipients. The 3Flex was then employed to measure the water uptake of these excipients over a broad range of activity. The subsequent use of krypton adsorption demonstrade the utility of these complex experiments of measuring the surface area both before and after exposure to water. A key feature of this protocol is the in situ handling of the excipients. Once a sample was loaded into a sample cell and connected to the 3Flex and of the analyses were conducted without removing the cell from the instrument. The 3Flex and the parallel analyses ensured the samples were not contaminated during transport or handling to obtain the isotherm data.

The Python programming language has been incorporated into the MicroActive for 3Flex software and this powerful scripting language allows users to develop extensions to the standard report library available within the 3Flex application. The use of python allowed us to implement new models like the GAB equation or express the adsorption data as mass of water sorbed in a rapid manner.

The Micromeritics 3Flex provides a flexible and extensible platform for material characterization.

References

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2. Robert B. Anderson. Modifications of the Brunauer, Emmett and Teller Equation. Jour-nal of the American Chemical Society, 68(4):686–691, 1946.
3. J. H. de Boer. The Dynamic Character of Adsorption, page 57. Clarendon Press, Oxford,1953.
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