3.3.1. TAP Reactor
The Temporal Analysis of Products (TAP) reactor is a kinetic setup that makes it possible to determine the thermodynamic constant of various materials onto different gases. The calculation of these data is possible following the measurements of the mean residence times of gas phase species. The accuracy of the thermodynamic constant depends on the sensitivity of this measurement.
Figure 34: Picture of the TAP-2 reactor (left) and the microreactor (right).
The TAP system, as shown in Figure 34, is composed of a valve-manifold assembly, an ultra-high vacuum system, a quadrupole mass spectrometer (QMS), a microreactor and a gas blending station. The valve-manifold assembly allows the injection onto the catalyst of a perfectly known pulse of a gas mixture (a few nanomoles) at high frequency, typically between 250 and 500 ȝs. The vacuum system decreases the pressure down to the range of 10-8 Torr. Since this setup has to allow the determination of the heat of adsorption at low coverage, the experiment is carried out in the Knudsen regime. Here, the detector is a QMS. To permit the study of the transition state, the detector is positioned at around 1 cm from the microreactor. The microreactor is a stainless steel fixed-bed reactor. It can be heated to around 700°C +/- 1°C. Typically, the catalyst loading is between 100 and 300 mg.
Meanwhile, the gas blending station is used for preparing accurate gas mixtures and producing constant gas flows. The principal difference between the TAP reactor and other kinetic setups comes from the pulse response experiment, with a narrow, perfectly characterized pulse injected into the microreactor. This experiment takes place in the Knudsen regime. An important characteristic of this regime is the independence between the diffusivity of the individual components of a mix and the gas composition. In order to attain this regime, it is necessary to work under high vacuum. Moreover, since the disturbance created by the injection of a small number of molecules onto the fixed-bed reactor is negligible, the kinetics corresponds to the constant kinetic state of the catalyst. In view of validating the results obtained by this method, all of the results are compared with those obtained by gravimetric analysis
3.3.2. Gravimetric Setup
The gravimetric analysis results are obtained by a Rupprecht & Patashnick TEOM 1500 pulse mass analyzer. The data are obtained from the variation of the catalyst mass during the adsorption under gas flow. Since this process is carried out in an attempt to validate the results of the TAP screening, only the adsorption of CO2
is studied. The TEOM analysis presents several advantages: a well-defined flow profile, eliminating possible diffusion and buoyancy phenomena; a very fast response time resolution (0.1 s); and a high mass resolution across the entire range of pressure and temperature. That said, the mechanical fragility of the setup makes this method of analysis incompatible with a screening approach. Typically, 70 mg of adsorbent sieved between 0.2 – 0.3 mm is pretreated at 550 K under He for each adsorption isotherm. During the experiment, the PCO2 varies from 0.2 to 133 kPa. In view of determining the heat of adsorption at low recovery, the data points obtained are fitted with the Langmuir-Hinshelwood equation. The entire set of results is also correlated with the grand canonical Monte Carlo simulation in collaboration with Northwestern University. In this study, only the simulation results, and not an explanation of the technique, are presented.
3.3.3. Modeling
The MOF particles are modeled as squared slabs with a characteristic length Lz
located in the macropores of the silica-alumina matrix. These particles are considered to be symmetrical. Reversible sorption takes place at the exterior of MOF particles and is described by an equation analogous to Henry’s law:
l A z z
A H C
C '
2
, / (1) where H' is the analogous Henry coefficient (mg3/ms3), CA is the reactant concentration (mol/m3) and z the MOF coordinate (m). Only the adsorbed molecules diffuse into the micropores. During TAP experiments, the concentration in the reactor remains very low and therefore the diffusion in the MOF pores is assumed to be
independent of the concentration and is therefore described by Fick's law. Inside the pores, first order irreversible reaction takes place on the acid sites.
The reactor is divided into three zones: two inert zones of quartz beads between which the catalyst is placed. The diffusion in all three zones is described by Knudsen diffusion. In the catalyst zone, the flux into the catalyst particles is included in the model. Actually, the MOF particles are located within a macroporous matrix.
However, the diffusion into the macropores is relatively fast and can therefore be lumped into the Knudsen diffusion coefficient according to the following equation114:
) / )) 1 ( ( 1
, (
b b p
K p
K
D D
H H
H
(2)
where DK, is the Knudsen diffusivity in the bed (m2/s), DK,p the Knudsen diffusivity in the pores of the particle (m2/s), p the particle porosity (mg3/ms3) and b the bed porosity (mg3/mr3). This leads to the following continuity equation for the catalyst zone:
z A z b A
p K A
b a J
x D C
t C
2 , 2
, (1 H )
H wG
w w
(3) where t is the time (s), x the reactor coordinate (m), az is the MOF surface area per volume (m2/m3) and JA,z (mol/m2 s) is the molar flux into the MOF as given by equation 3:
2 , 2 ,
, z
D C
JAz zeff Az w w
(4) where Dz,eff is the effective Knudsen diffusivity (m2/s) in the MOF.
Parameter estimation was performed by fitting the entire simulated response curve to the experimental one in the time domain. For each curve, the sum of the squared deviations over 400 data points was used as the objective function which was minimized using an algorithm based on Marquardt’s method115. Diffusion and sorption parameters were determined simultaneously by matching the simulated response curves of the hydrocarbons to the experimentally obtained ones at low
parameters were estimated from the response curves at temperatures from 773 to 923 K, fixing the diffusion and sorption parameters at the values determined at low temperatures. For the regression analysis, a reparameterized form of the Arrhenius and Van 't Hoff equations was used. A full statistical analysis, which included the calculation of the 95% confidence intervals on the estimated parameters, was performed after regression.