BET Surface Area Measurement

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Rutgers University

Department of Ceramic & Materials Engineering

Laboratory 254: M2

BET Surface Area Measurement

Glenn K. Lockwood

Lab date: February 7, 2005Professor Richard E. Riman

TAs: David Babson, Milca Aponte


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Abstract

In this experiment, a BET analyzer was used to measure the specific surface areas of

hydroxyapatite and trabecular bone using nitrogen gas, and these figures were then compared to

the specific surface areas of previously measured samples of titania and cortical bone. The data

collected from the analysis was highly consistent and fit the BET equation remarkably well, and

it was from this information that the specific surface areas were calculated. Thus, the

applicability of the BET equation to measuring the specific surface areas of hydroxyapatite,

titania, trabecular bone, and cortical bone was affirmed.


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Introduction

In the field of material processing, the majority of chemical reactions that are of great

significance are heterogeneous, meaning they occur in multiphase systems. As such, these

reactions can only take place where the two reactants meet at the phase boundaries, and many of

the more important processes in material science involve solid reactants in some way or another.

In these cases, it only makes sense that maximizing the surface area of a solid reactant to

maximize the rate of reaction would be of paramount importance, as the larger the phase

interface, the more product can be formed at once and the more economical the process is. A

perfect example of this are the nanostructured catalysts that, due to their extremely high active

surface area, are currently being researched in hopes that they may lead the way to the large-

scale production of hydrogen gas from biomass for use as a clean energy source[1]. Other areas

in which high surface area materials are being used and studied in are petroleum processing,

chemical separation applications, various biotechnology applications, and advanced chemical

sensing technology[2].

Thus, being able to identify and characterize high surface area materials is of great

interest in material science and engineering; knowing the exposed surface area per gram of

material can help determine if a certain reaction is economically feasible before ever having to

expend the money, time, and labor required to physically test it. However, making such

measurements becomes relatively difficult when dealing with nanoparticles that have high

specific surface areas. One of the more popular methods of making such measurements involves

coating such high surface area materials in a single layer of nitrogen atoms at the freezing point

of nitrogen; after this monolayer of nitrogen is formed, the sample can then be removed from the


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nitrogen atmosphere and heated, causing the adsorbed nitrogen to jump off of the material and

be measured. The area covered by the adsorbed nitrogen is then the surface area of the material.

Unfortunately, such a process is not feasible in reality because the nitrogen does not only

adsorb to the materials surface, but to other nitrogen atoms that have already been adsorbed as

well. This creates an uneven covering over the surface of the material, leaving some spots

covered by only a single atom while others may have multiple nitrogen atoms stacked onto each

other. Taking this volume of nitrogen to be equivalent to the amount required to coat the

material being tested entirely would give erroneously large results since more nitrogen was

adsorbed than it would take to create a single monolayer. However, an equation was developed

by Stephen Brunauer, Paul Emmett, and Edward Teller which included correctional factors that

made this method incredibly useful[3]. The equation is described as

00

)1(1

)( P

P

CV

C

CVPPV

P

mm

+=

y = b + m x

where P0is the saturation pressure of the gas (atmospheric pressure if the process is carried out at

the boiling point of nitrogen at atmospheric pressure), V is the volume of gas adsorbed per unit

mass of material at pressure P, Vmis the volume of gas required to cover a unit mass of the

material with a complete monolayer of gas atoms, and C is a constant.

This BET equation can also be plotted as a linear equation from which value for the

volume of gas required to form a complete monolayer can be extracted. Knowing this volume,

the specific surface area of the material tested can then be derived using other more basic

formulas. In this experiment, this process is carried out for several different materials to

compare specific surface area values using a BET instrument which operates using nitrogen as

the adsorbate.


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Procedure

Before entering the lab, three sample tubes had been cleaned and each filled with a

sample of either hydroxyapatite, cortical bone, or trabecular bone. These tubes were then

massed, degassed, and massed again and the BET analyzer configured and its dewar flask filled

with liquid nitrogen and set into place. Thus, all that had to be done in the laboratory was load

each degassed sample and collect the results of the analysis.

The first sample to be tested was the trabecular bone; the tube containing it was loaded

into the analyzer, the sample ID, mass, and density entered into the software, and the machine set

to make five measurement points. The machine was then activated and, after the sample was

finished, it was removed from the machine and the resulting data saved to disk. The sample of

degassed hydroxyapatite was then massed and the analysis procedure repeated. The cortical

bone sample was not analyzed due to time constraints.

Results and Discussion

Of the two samples tested in the laboratory (the trabecular bone and hydroxyapatite), the

titania sample tested beforehand, and the results obtained from a previous testing of cortical

bone, all of the results were remarkably precise and conformed to the mathematical relationships

described by the BET equation. Figure 1 displays a superposition of all of the data measured by

the BET machine and the linear best fit lines for them. The functions that describe these best fit

lines are based on multiple points and are determined statistically based on the empirical data; as

can be seen from the plots, each set of data obtained is highly linear when plotted in the form of

the BET equation.


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From these linear regression lines, the unknown factors in the BET equation (namely, C

and Vm) can be equated to the terms in the linear regression function and solved as a simple

system of equations. For example, by knowing the BET equation

00

)1(1

)( P

P

CV

C

CVPPV

P

mm

+=

and its counterparts in linear form (y = mx + b)

)( 0 PPV

Py

= ,CV

Cm

m

)1( = ,

0P

Px = , and

CVb

m

1= ,

a data plot can be made simply by plotting the measured values for P/Poon the x-axis andP/V(Po-P)

on the y-axis. This is possible because all of the terms in these x- and y-equivalencies are

known; P is the known pressure the machine lets into the sample tube during each run, P0is the

vapor pressure of the nitrogen at the temperature of the material (which is at the boiling

temperature of nitrogen, so the vapor pressure simply is equal to atmospheric pressure), and V is

the measured volume of the nitrogen multilayer that was adsorbed to the surface of the material.

After a point is plotted for each testing run made on a sample, the line of best fits slope

then is equal to m =(C-1)/VmCand its y-intercept is equal to b =1/VmC. Thus, mand bare a system

of two equations and two unknowns (C and Vm), both of which can be solved. Once Vmis

calculated, applying it to the equation

Total Surface Area =2240

0 mAVNa

where a0is the cross-sectional area of a nitrogen atom and NAis Avogadros number will give

the surface area of the entire sample being tested. Dividing this surface area by the mass of the

sample then yields the specific surface area of the material.


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Considering the BET surface area calculations that resulted from this experiment as

shown in Figure 2, it is clear that hydroxyapatite has a specific surface area that far surpasses the

other three materials that data was obtained for. Titania powder also was found to have a fairly

large specific surface area, while the two natural bone samples had the lowest specific surface

areas. Of particular interest in Figure 2, though, are the error bars. Barely visible (with the

largest percent standard error being in the hydroxyapatite measurement, which had a specific

surface area of 76.6471 0.5099 m2/g), these very small error margins also indicate that the data

obtained by the BET analysis machine was highly consistent.

One final observation that is reflected in the data and proven in the math of the BET

equation was that materials with higher surface areas also had the largest volume of nitrogen

adsorbed to a multilayer on their surfaces. Thus, no material tended to irregularly attract more

nitrogen atoms than any other, and a definite proportionality exists between specific surface area

and amount of nitrogen adsorbed to the surface in a multilayer. While not entirely useful when

examining just one material, this principle could be used to compare the relative specific surface

areas of different materials without having to actually calculate them. For example, because the

y axis in Figure 1 is proportional to the inverse of the volume adsorbed, it is obvious that the

materials with the lowest relative data sets and thus the highest volumes of nitrogen adsorbed

(such as hydroxyapatite and titania) would have generally higher specific surface areas than the

materials with the higher data sets, such as the trabecular and cortical bones.


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Conclusion

Based on the data collected before and during this experiment, it is clear that

hydroxyapatite has the most specific surface area of all of the materials tested. Titania also has a

relatively high specific surface area, while trabecular bone and cortical bone have the lowest

specific surface areas of the four. Furthermore, the data collected from the BET machine, when

plotted in the form of the BET equation, displays a highly linear trend from which the volume of

a nitrogen monolayer can be extracted. The standard deviation displayed by the data points from

this trendline is incredibly small as well, reaffirming the validity of using the BET equation to

obtain specific surface area measurements as well as exemplifying the high degree of precision

in using a BET analysis machine.


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Appendix

Figure 1:Results of BET Analysis for Tested Materials

y = 0.0567x + 0.0001

y = 0.0997x + 0.0007

y = 0.1804x + 0.007

y = 0.5144x + 0.0153

0.000000

0.020000

0.040000

0.060000

0.080000

0.100000

0.120000

0.140000

0.160000

0.180000

0.00000

0

0.05000

0

0.10000

0

0.15000

0

0.20000

0

0.25000

0

0.30000

0

0.35000

0

P/Po

P/V(Po-P)

Titania Trabecular Bone Hydroxyapatite

Cortical Bone Linear (Hydroxyapatite) Linear (Titania)Linear (Cortical Bone) Linear (Trabecular Bone)

This is a plot of the five steps made in the analysis of the three materials tested (titania,

trabecular bone, and hydroxyapatite) and the results obtained from a previous testing of cortical

bone. As roughly indicated by the graphs, the plotted points are all very close to being linear.


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Figure 2: Specific Surface Areas as Calculated by the BET Method

0

10

20

30

40

50

60

70

80

90

Titania Trabecular Bone Hydroxyapatite Cortical Bone

BETSurfaceArea(m^2/g)

This is a comparison of the specific surface areas obtained by using the BET analysis machine on

four materials. Also plotted are error bars indicating the specific error of the five passes made

for each materials; however, these error margins are so narrow that they are hard to see.


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Works Referenced

1. Catalysis. Copyright 2005 Dictionary and Atlas of

Nanoscience and Nanotechnology.

2. Stucky, Galen D., High Surface Area Materials.

Copyright 1998 Galen D. Stucky.

3. Laboratory II Handbook. BET Surface Area Measurement, p.11

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BET Surface Area Measurement