.
Angewandte
Communications
described above, we formulated a simple statistical mechan-
ical approach (see Supporting Information). The model
assumes host–guest and guest–guest interactions within
a cavity and incorporates cavity deformation as well as elastic
coupling between neighboring cavities in a one-dimensional
crystal. A reduced version of this model, intended to
represent the CO2 sorbing system, assumes that host–guest
and guest–guest interactions occur, but that host deformation
is negligible (Supporting Information). The calculations for
both systems are analogous to that of a standard lattice gas
derivation of the adsorption isotherm,[11] with host deforma-
tion determining the interaction between nearest sites (much
related work[12] has been applied in different contexts to
elastic lattice gases). They yield the total occupancy as
a function of pressure, as well as the contribution to total
occupancy by singly and doubly filled voids (Figure 2). The
full model represents the C2H2 sorbing system, but is also
applicable to CO2. Assuming reasonable elastic constants and
using calculated interaction energies (Supporting Informa-
tion), the inflection in the overall sorption isotherm (as
observed experimentally for acetylene) becomes apparent
(Figure 2b). The qualitative origin of this feature represents
the excess energy required to add a second molecule to
a singly occupied cavity as deformation of the surrounding
voids is taken into account. As filling of the voids continues,
further occupation is eased because much of the required
deformation has already taken place through elastic coupling
to already filled voids. The model also enables the derivation
of expressions for the contributions due to singly and doubly
occupied cavities to the total occupancy that can then be
superimposed on the experimental data. Upon applying two
fitting parameters, the model agrees almost exactly with the
experimental data. We note, however, that steps have also
been observed for open frameworks and host distortion is
therefore not exclusively responsible for inflections[13] present
in sorption isotherms.
We have developed a relatively simple procedure suitable
for routine single-crystal structure analysis with the sample
exposed to controlled gas pressures. As a proof of concept,
a series of “pressure-lapse” crystal structure snapshots was
recorded to smoothly track subtle changes resulting from gas
loading by a porous host. These experiments are analogous to
the measurement of a sorption isotherm, but provide detailed
structural information regarding the underlying mechanism
of the gas uptake process. We observed that carbon dioxide
and acetylene are accommodated in different orientations
within the available space and were able to rationalize this on
the basis of intermolecular host–guest interactions and space
filling considerations.[8h] Furthermore, we have utilized our
observations both quantitatively and qualitatively to formu-
late a statistical mechanical model that accounts for the
shapes of the experimental sorption isotherms. These models
allow deconvolution of the total occupancy into components
representing the statistical distributions of the three possible
occupancy states for a representative cavity with a maximum
possible occupancy of two guest molecules. Future routine
application of our systematic method in conventional SCD
laboratories promises to yield significant advances in the field
of gas sorption studies by providing an improved under-
standing of the processes that occur at the molecular level.
Received: February 15, 2012
Published online: && &&, &&&&
Keywords: acetylene · carbon dioxide · flexible pores ·
.
gas sorption · inclusion compounds
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ꢀ 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2012, 51, 1 – 5
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