In [1]:
%run import.ipynb
We use the area_BET function, and we first want to look at how the framework attempts to calculate the good BET region on its own. For this we pass the verbose parameter and then use matplotlib to display the graph.
In [2]:
isotherm = next(i for i in isotherms_n2_77k if i.material=='MCM-41')
print(isotherm.material)
pygaps.area_BET(isotherm, verbose=True)
plt.show()
It looks that the correlation is reasonably good. A warning is emmited if this is not the case. We can also restrict the pressure range manually to see what difference it would make.
In [3]:
pygaps.area_BET(isotherm, limits=(0.05, 0.2), verbose=True)
plt.show()
Now let's do the analysis on all of the nitrogen samples. Instead of sequential calculations, we'll assume the framework makes a reasonably accurate choice. The function returns a dictionary with all the calculated parameters, so we'll just select the BET area from there.
In [4]:
results = []
for isotherm in isotherms_n2_77k:
results.append((isotherm.material, pygaps.area_BET(isotherm)))
[(x, y['area']) for (x,y) in results]
Out[4]:
We also have isotherms which were measured with $CO_2$ at room temperature. While there's no guarantee that the BET method is still applicable with this adsorbate and temperature, the framework can still attempt to perform the calculations.
It just happens that the carbon sample is the same in both isotherms. Let's see how the $CO_2$ BET surface area looks.
In [5]:
isotherm = next(i for i in isotherms_calorimetry if i.material=='Takeda 5A')
print(isotherm.material)
pygaps.area_BET(isotherm, verbose=True)
plt.show()
The surface area obtained with carbon dioxide is around 780 $m^2$. Compared to the nitrogen surface area of 1100 $m^2$, it is much smaller. While the checks implemented did not find anything wrong, this is likely due to interactions between carbon dioxide and the carbon surface leading to the breakdown of the BET theory.
While any kind of adsorbate and temperature can be analysed through the framework, result interpretation is left at the discretion of the user. More info can be found in the documentation of the module.
Another common method of calculating specific surface area relies on fitting the isotherm with a Langmuir model. This model assumes adsorption is confined to a single layer. We use the area_langmuir function, and we first want to see the range selected by the standard method. For this we pass the verbose parameter and then use matplotlib to display the graph.
In [6]:
isotherm = next(i for i in isotherms_n2_77k if i.material=='MCM-41')
print(isotherm.material)
pygaps.area_langmuir(isotherm, verbose=True)
plt.show()
The correlation is not very good due to the mesopore condensation which is not predicted by the Langmuir model. Due to this, the area calculated is not realistic. We can select the a range in the monolayer adsorption regime for a better fit.
In [7]:
print(isotherm.material)
pygaps.area_langmuir(isotherm, limits=(0.05, 0.3), verbose=True)
plt.show()
The fit is now better and the calculated area is also realistic. Comparing it to the BET area obtained previously, we see that it is higher by about 150 m2. Since adsoprtion is happening in multiple layers rather than a monolayer, it is likely that the value for complete coverage overshoots the actual value. In general the Langmuir surface area is not as widely applicable as the BET one.
Now let's do the analysis on all of the nitrogen samples and compare the obtained surface areas with the BET ones.
In [8]:
area_langmuir = []
area_langmuir_lim = []
area_bet = []
for isotherm in isotherms_n2_77k:
area_bet.append(pygaps.area_BET(isotherm)['area'])
area_langmuir.append(pygaps.area_langmuir(isotherm)['area'])
area_langmuir_lim.append(pygaps.area_langmuir(isotherm, limits=(0.01, 0.3))['area'])
fig, (ax1, ax2) = plt.subplots(1,2, figsize=(10,5))
ax1.scatter(area_langmuir, area_bet)
ax2.scatter(area_langmuir_lim, area_bet)
ax1.set_title('BET v Langmuir area, full range')
ax2.set_title('BET v Langmuir area, low pressure range')
ax1.set_xlim(left=0, right=2000)
ax1.set_ylim(bottom=0, top=2000)
ax2.set_xlim(left=0, right=2000)
ax2.set_ylim(bottom=0, top=2000)
ax1.set_xlabel('Langmuir surface area')
ax1.set_ylabel('BET surface area')
ax2.set_xlabel('Langmuir surface area')
ax2.set_ylabel('BET surface area')
plt.show()
We can see that some points correspond, while others are not as well correlated. Unless the adsorption isotherm respects the Langmuir model, the calculated surface areas do not match. However, if the Langmuir area is calculated in a low pressure regime, ideally before multilayer adsorption or condensation occurs, the two specific areas are better correlated (right graph).
More info can be found in the documentation of the module.