be explained considering that a rapid change in the fluid concentration corresponds
to slow mass transport out of the particles.
Differently from the case of the Na,Cs-Rho sample, this discrepancy cannot be
linked exclusively to the non-linearity of the isotherm, since the shape of the
isotherm does not differ considerably from the one of Na,Cs-Rho [18]. Moreover,
a careful observation of the initial part of the experimental curve shows a difference
in the shape of the curve between the full and partial loading case; this cannot be
related simply to the non-linearity on the ZLC response. The trend observed
indicates that a second contribution influences the response of this system. Independent in situ XRD measurements of CO 2 adsorption proved that structural changes
occur in Na-Rho with variable CO 2 loading: the size of the 8MR windows increases
from 2.26 Å in the dehydrated form to 2.75 Å at partial pressure of CO 2 of 0.1 bar,
resulting in a faster diffusion of CO 2 at higher coverages [18]. The fact that this
effect is visible in the ZLC experiments indicates that the time constant of the
structural change is comparable to that of the diffusion of CO 2 through the sample.
As the CO 2 desorbs from the sample, emptying the cages, the 8MR windows switch
from the large to the restricted size. This is reflected in the time constant of the CO 2 .
Should the structural change be a much slower process, a faster diffusivity
(corresponding to the original structure) would have been observed. If the structural
change was much faster, then the external layer of the crystals would rearrange
rapidly to the final configuration, and the measured curve would have been very
similar to a single diffusion process.
To confirm this hypothesis, a low-concentration ZLC experiment was carried out.
In this experiment the sample was fully equilibrated with a feed mixture with just 1%
of CO 2 : the aim is to operate the system at a sorbate concentration low enough to
exclude the contribution of the non-linearity. More importantly, in these conditions
the low concentration of CO 2 should induce only minor changes in the structure of
the framework.
The experiment is reported in Fig. 14, where the same time constant obtained
from the experiment at 10% of CO 2 was used to predict the experimental data at 1%.
Clearly, the model allows to predict the experimental data in the entire range of
concentrations, indicating that in these conditions, the desorption process is
governed by a single time constant, i.e. a single structure.
The good prediction of the partial loading experiment in Fig. 14 indicates that,
due to the diffusional resistance, the average concentration inside the solid is below
the one that would induce structural modifications: the operating conditions should
not differ much from the ones of the experiment at 1% of CO 2 . For this reason, it
becomes interesting to compare the predicted profile of the adsorbed phase concentration between the three cases of interest: full saturation at 10% and 1% of CO 2 and
partial saturation.
The ZLC model can be solved with respect to the adsorbed phase concentration,
and one can also predict, based on the diffusivity, the adsorbed concentration profile
inside the crystal as function of the radius of the particle [9]. Figure 15 shows the
predicted adsorbed concentration profiles inside the crystal for the partially and fully
equilibrated cases at different desorption times: the curves were obtained using the
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E. Mangano and S. Brandani
to slow mass transport out of the particles.
Differently from the case of the Na,Cs-Rho sample, this discrepancy cannot be
linked exclusively to the non-linearity of the isotherm, since the shape of the
isotherm does not differ considerably from the one of Na,Cs-Rho [18]. Moreover,
a careful observation of the initial part of the experimental curve shows a difference
in the shape of the curve between the full and partial loading case; this cannot be
related simply to the non-linearity on the ZLC response. The trend observed
indicates that a second contribution influences the response of this system. Independent in situ XRD measurements of CO 2 adsorption proved that structural changes
occur in Na-Rho with variable CO 2 loading: the size of the 8MR windows increases
from 2.26 Å in the dehydrated form to 2.75 Å at partial pressure of CO 2 of 0.1 bar,
resulting in a faster diffusion of CO 2 at higher coverages [18]. The fact that this
effect is visible in the ZLC experiments indicates that the time constant of the
structural change is comparable to that of the diffusion of CO 2 through the sample.
As the CO 2 desorbs from the sample, emptying the cages, the 8MR windows switch
from the large to the restricted size. This is reflected in the time constant of the CO 2 .
Should the structural change be a much slower process, a faster diffusivity
(corresponding to the original structure) would have been observed. If the structural
change was much faster, then the external layer of the crystals would rearrange
rapidly to the final configuration, and the measured curve would have been very
similar to a single diffusion process.
To confirm this hypothesis, a low-concentration ZLC experiment was carried out.
In this experiment the sample was fully equilibrated with a feed mixture with just 1%
of CO 2 : the aim is to operate the system at a sorbate concentration low enough to
exclude the contribution of the non-linearity. More importantly, in these conditions
the low concentration of CO 2 should induce only minor changes in the structure of
the framework.
The experiment is reported in Fig. 14, where the same time constant obtained
from the experiment at 10% of CO 2 was used to predict the experimental data at 1%.
Clearly, the model allows to predict the experimental data in the entire range of
concentrations, indicating that in these conditions, the desorption process is
governed by a single time constant, i.e. a single structure.
The good prediction of the partial loading experiment in Fig. 14 indicates that,
due to the diffusional resistance, the average concentration inside the solid is below
the one that would induce structural modifications: the operating conditions should
not differ much from the ones of the experiment at 1% of CO 2 . For this reason, it
becomes interesting to compare the predicted profile of the adsorbed phase concentration between the three cases of interest: full saturation at 10% and 1% of CO 2 and
partial saturation.
The ZLC model can be solved with respect to the adsorbed phase concentration,
and one can also predict, based on the diffusivity, the adsorbed concentration profile
inside the crystal as function of the radius of the particle [9]. Figure 15 shows the
predicted adsorbed concentration profiles inside the crystal for the partially and fully
equilibrated cases at different desorption times: the curves were obtained using the
138
E. Mangano and S. Brandani