NMR studies of methane and hydrogen in microporous materials
We review the results of nuclear magnetic resonance studies of the molecular dynamics of the quantum gases HD and CH₄ adsorbed in the cages of microporous structures. Measurements of the variation of the nuclear spinlattice and nuclear spin-spin relaxation times with temperature provide detailed i...
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irk-123456789-1284562018-01-10T03:03:03Z NMR studies of methane and hydrogen in microporous materials Hamida, J.A. Tang, Y. Sullivan, N.S. Ji, Y. Пористые и низкоразмерные структуры We review the results of nuclear magnetic resonance studies of the molecular dynamics of the quantum gases HD and CH₄ adsorbed in the cages of microporous structures. Measurements of the variation of the nuclear spinlattice and nuclear spin-spin relaxation times with temperature provide detailed information about the translational and rotational dynamics of the adsorbed molecules over a wide temperature range. 2016 Article NMR studies of methane and hydrogen in microporous materials / Y. Ji, J.A. Hamida, Y.Tang, N.S. Sullivan // Физика низких температур. — 2016. — Т. 42, № 2. — С. 105–108. — Бібліогр.: 24 назв. — англ. 0132-6414 PACS: 76.60.–k http://dspace.nbuv.gov.ua/handle/123456789/128456 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Пористые и низкоразмерные структуры Пористые и низкоразмерные структуры |
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Пористые и низкоразмерные структуры Пористые и низкоразмерные структуры Hamida, J.A. Tang, Y. Sullivan, N.S. Ji, Y. NMR studies of methane and hydrogen in microporous materials Физика низких температур |
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We review the results of nuclear magnetic resonance studies of the molecular dynamics of the quantum gases
HD and CH₄ adsorbed in the cages of microporous structures. Measurements of the variation of the nuclear spinlattice
and nuclear spin-spin relaxation times with temperature provide detailed information about the translational
and rotational dynamics of the adsorbed molecules over a wide temperature range. |
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Article |
| author |
Hamida, J.A. Tang, Y. Sullivan, N.S. Ji, Y. |
| author_facet |
Hamida, J.A. Tang, Y. Sullivan, N.S. Ji, Y. |
| author_sort |
Hamida, J.A. |
| title |
NMR studies of methane and hydrogen in microporous materials |
| title_short |
NMR studies of methane and hydrogen in microporous materials |
| title_full |
NMR studies of methane and hydrogen in microporous materials |
| title_fullStr |
NMR studies of methane and hydrogen in microporous materials |
| title_full_unstemmed |
NMR studies of methane and hydrogen in microporous materials |
| title_sort |
nmr studies of methane and hydrogen in microporous materials |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2016 |
| topic_facet |
Пористые и низкоразмерные структуры |
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http://dspace.nbuv.gov.ua/handle/123456789/128456 |
| citation_txt |
NMR studies of methane and hydrogen in microporous materials / Y. Ji, J.A. Hamida, Y.Tang, N.S. Sullivan // Физика низких температур. — 2016. — Т. 42, № 2. — С. 105–108. — Бібліогр.: 24 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT hamidaja nmrstudiesofmethaneandhydrogeninmicroporousmaterials AT tangy nmrstudiesofmethaneandhydrogeninmicroporousmaterials AT sullivanns nmrstudiesofmethaneandhydrogeninmicroporousmaterials AT jiy nmrstudiesofmethaneandhydrogeninmicroporousmaterials |
| first_indexed |
2025-07-09T09:07:49Z |
| last_indexed |
2025-07-09T09:07:49Z |
| _version_ |
1837159753429549056 |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 2, pp. 105–108
NMR studies of methane and hydrogen in microporous
materials
Yu Ji, J.A. Hamida, Yibing Tang, and N.S. Sullivan
Department of Physics, University of Florida, Gainesville, FL, USA
E-mail: sullivan@phys.ufl.edu
Received September 7, 2015, published online December 23, 2015
We review the results of nuclear magnetic resonance studies of the molecular dynamics of the quantum gases
HD and CH4 adsorbed in the cages of microporous structures. Measurements of the variation of the nuclear spin-
lattice and nuclear spin-spin relaxation times with temperature provide detailed information about the transla-
tional and rotational dynamics of the adsorbed molecules over a wide temperature range.
PACS: 76.60.–k Nuclear magnetic resonance and relaxation.
Keywords: magnetic resonance, microporous materials, quantum gases HD and CH4.
1. Introduction
The absorption and dynamics of H2 and CH4 among
other light gases (CO, CO2, N2…) when confined to the
internal cages of mesoporous structures has received
great interest in recent years because of the potential use
of these mesoporous materials (MOFs, MCM, zeolites...)
for the storage and transport of commercially important
gases [1–7]. The efficiencies of various nanoporous and
microporous materials for storage and ease of removal de-
pend crucially on the thermodynamic properties of these
gases at or near the surfaces of the chosen materials [8–12].
These properties and the characteristic dynamics are also
important in the development of methods for CO2 sequestra-
tion [13–15]. There is considerable documentation in the
literature about the total absorption properties of light gases
(such as hydrogen and methane) on various porous materials
but there is little information about the detailed dynamics of
the gases in the confined geometries or about their interac-
tions with the walls of the confinement. One of the great
advantages of the use of NMR techniques is that they can
address this need. In this paper we review recent applica-
tions of NMR methods to study the dynamics of CH4 and
HD in microporous materials [16–19].
2. Experimental methods
Careful NMR techniques can be very powerful tools for
measuring the dynamics of molecules in condensed matter
systems. The motion of the molecules modulates the nu-
clear dipole-dipole interactions between the spins of the
molecules as well as the interactions between the spins of
the mobile molecules and the magnetic spins in the walls
of the porous adsorbers. The Fourier components of these
fluctuations at = Lω ω , the nuclear Larmor frequency, can
induce transitions between the nuclear spin levels of the
molecules and this will determine the nuclear spin-lattice
relaxation times. In order to calculate the relaxation times
we follow Cowan [20] and express the dipolar spin-spin
interactions in terms of irreducible components
2
dip
= 2
= m
m
H D
−
∑ , (1)
where for like spins
2 4
30
2 2= ( ) ( )/
4 5
m m
m ij ij
ij
D Y T ij r−µ γ
Ω
π ∑ , (2)
0µ is the permeability of free space, γ is the nuclear gyro-
magnetic ratio of the nucleus, 2 ( )m
ijY Ω is the spherical
harmonic for the angles = ( , )ij ij ijΩ θ ϕ specifying the ori-
entation of the vector ijr with respect to the applied mag-
netic field, ijθ is the polar angle and ijϕ is the azimuthal
angle for the vector ijr . The 2 ( )mT ij are irreducible nuclear
spin operators that transform under rotation in the same
manner as the spherical harmonics:
0
2 ( ) = 3 z z
i j i jT ij I I I I⋅ − , (3)
1
2
3( ) = [ ]
2
z z
i j i jT ij I I I I+ ++ , (4)
2
2
3( ) =
2 i jT ij I I+ +− , (5)
with †
2 2( ) = ( ) [ ( )] .m m mT ij T ij− −
© Yu Ji, J.A. Hamida, Yibing Tang, and N.S. Sullivan, 2016
Yu Ji, J.A. Hamida, Yibing Tang, and N.S. Sullivan
In the simplest cases where a single correlation time for
the fluctuations dominates one can obtain a direct measure
of the microscopic motion:
2
2
1 =1,2
1 2= ( )
3 n L
n
M n J n
T
ω∑ , (6)
where 2M is the second moment of the nuclear spin inter-
actions and ( )nJ ω is the Fourier component of the autocor-
relation functions for the dipolar interactions given by
*
2 2( ) = ( ) (0)n n nG t Y t Y .
This simple case often occurs for the translational and
rotational diffusion of molecules in condensed phases. If
the motion is characterized by a unique correlation time,
,cτ as for example, given by the microscopic jump time
from one lattice site to a neighboring site in the case of
translational diffusion, the NMR measurements can deter-
mine the correlation time and thus the diffusion constant
2 1
0( cD za −τ , where 0a is the lattice spacing and z the co-
ordination number). These times inferred from NMR
measurements can be compared with those deduced from
neutron scattering measurements. In addition to the spin-
lattice relaxation time one can also measure the nuclear
spin-spin relaxation times, 2T . These times are determined
by the Fourier component at close to = 0ω . Specifically,
2
2
2 = 2
1 1= (6 ) ( ).
4 n L
n
n J n
T −
− ω∑ (7)
In the case of a unique correlation time for the motion,
as is often the case for motions associated with quantum
jumping in adsorbed gases we can simplify Eqs. (6) and
(7). For rapid motion where the correlation time 1<<c L
−τ ω
we have
2
1 2
1 1 10= =
3 cM
T T
τ . (8)
In the opposite case of slow motions, for which <<c Lτ ω ,
we have
2
2
1
1 4= ,
3 L c
M
T ω τ
(9)
2
2
1 = cM
T
τ . (10)
In many cases at low temperatures there can be several
sources of excitations; phonons, spin-interactions, quantum
diffusion, and the different interactions can form weakly
coupled energy reservoirs. In this situation the relaxation
will depend on the couplings between the respective ener-
gy baths associated with these excitations as illustrated in
Fig. 1 where XYR represents the relaxation rate between
baths X and Y .
If the energy baths can attain thermal equilibrium in a
time short compared to the relaxation couplings between
the baths, the relaxation time observed experimentally will
vary with changes in the heat capacities of the individual
baths. In Fig. 1 we show the case where the coupling BCR
is the slowest (or weakest) connection for the energy flow.
In this case the observed relaxation time will be
1,observed = A B
BC
B
C CT T
C
+
, (11)
where ,AC BC are the heat capacities of baths A and B .
When this situation occurs, the experiments often show a
two-stage relaxation process: (i) a short-time relaxation as
an energy bath comes into internal thermal equilibrium
after a disturbance, and (ii) a long-time component to the
relaxation determined by cross-relaxation between differ-
ent energy baths.
3. Experimental observations
Prior to the NMR studies the mesoporous substrate ma-
terials were all first characterized by measuring the adsorp-
tion isotherm at a fixed temperature. A typical example for
methane adsorbed on zeolite is shown in Fig. 2 for a sam-
ple maintained at 77 K. Small gas volumes are adsorbed
sequentially and the equilibrium pressure at each step is
recorded as one point on the graph. The observation of at
least two steps in the isotherm is a measure of a high-
quality surface.
Fig. 1. Illustration of different weakly coupled energy baths des-
ignated by A, B and C where the weakest coupling is the vertical
path between B and C.
Fig. 2. Experimental isotherm for methane on zeolite 13X. (After
Fig. B1 from Ref. 19.)
106 Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 2
NMR studies of methane and hydrogen in microporous materials
3.1. Adsorbed methane
Studies of the relaxation of the nuclear spins of methane
adsorbed on zeolite 13X show unexpected features, namely
the existence of two prominent peaks in the temperature
dependence below 65 K. These peaks are believed to result
from the existence of rotational energy levels associated
with the tetrahedral molecules, associated with the A, E
and T representations of the tetrahedral group dT . The
ground state is the A-state with total nuclear spin = 2I
and the next level is the T-state with =1I . The E-state
with = 0I is not relevant for the nuclear spin relaxation
rate. For adsorbed molecules the E-state can split into
separate A- and T-states for sites with trigonal symmetry
as is the case for molecules near some of the faces in the
zeolite cages. The solid red line shown in Fig. 3 is a fit
for two distinct T-states using Eq. (10) with heat capacities
3= ,
2A A BC Ng k (12)
2
2= sech
2 2i i
i i
T T BC Ng k
T T
∆ ∆
(13)
for the A- and Ti-states, respectively. Ag and iTg are the
degeneracies of the A- and Ti-states, respectively. The best
fit is obtained for two T-states with energies 1 = 25∆ K and
2 = 55∆ K, as represented by the red line in Fig. 3.
At high temperatures one observes a straightforward
thermal activation for the nuclear spin-lattice relaxation
times and that is expected for the translational degrees of
freedom of the molecules. The best description of the ex-
perimental points is obtained using Eq. (6) with a
Lorentzian spectral density of the form
2( ) =
1 ( )
J n
n
τ
ω
+ ωτ
(14)
with the correlation time τ given by the molecular jump
time
/act0= eE Tτ τ (15)
with 0 =τ 7.1⋅10–13 s and act = (2600 260)E ± K. This fit is
given by the green line of Fig. 3. The activation energy
compares favorably with the results of Monte Carlo simu-
lations reported by Yashoanth et al. [21]. The rounded
minimum at 78 K in the solid green curve of Fig. 3 is the
BPP minimum [22] that arises when the Larmor frequency
and the molecular motional frequencies are equal.
3.2. HD on zeolite 13X and Z-MOF
The dynamics of HD molecules has been studied for
two types of structures, zeolite 13X and the metal organic
framework Z-MOF. HD was explored rather than H2 be-
cause of the difficulties associated with the ortho-para
conversion of H2 and consequent uncertainty of the ortho-
H2 concentration as a sample ages. The nuclear relaxation
data for HD is also more straightforward to interpret be-
cause only translational degrees of freedom are relevant.
At high temperatures we see a simple thermal activation
of the translational diffusion of the molecules as shown in
Fig. 4. The solid red line of Fig. 4 is found from Eq. (9)
with /act0= eE T
cτ τ , 0 =τ 6.7⋅10–13 s and act = (73 3)E ± K.
These values for cτ correspond to a translational diffusion
constant of D = (8.2±2.8)⋅10–6 cm2/s at T = 19.5 K which
is comparable to the values observed by Coulomb et al.
[23] using neutron scattering techniques.
One of the unexpected results of the studies was the
observation of peaks in the dependence of the nuclear
spin-lattice relaxation times at low temperatures for HD
on zeolite. This behavior is illustrated in Fig. 5. These
peaks suggest that there is a discreet set of energy levels
for the translational motion and that these levels contrib-
Fig. 3. (Color online) Variation with temperature of the spin-lattice
relaxation times of methane adsorbed on zeolite. The solid red line
represents the contribution of the Schottky specific heats of the
rotational states of methane, and the solid green line is the calculat-
ed variation for thermally activated translational motion in the zeo-
lite cage. (Reproduced with permission from Fig. 4 of Ref. 16.)
Fig. 4. Dependence of the nuclear spin-spin relaxation times with
temperature for HD adsorbed on zeolite 13X. The solid line cor-
responds to a calculated variation for a thermal activation energy
of (72±3) K. (After Fig. 9 of Ref. 19.)
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 2 107
Yu Ji, J.A. Hamida, Yibing Tang, and N.S. Sullivan
ute to peaks in the heat capacity. From Eq. (6) we expect a
corresponding set of peaks in the values of T1 at the tem-
peratures corresponding to those energies. For a particle in
a potential well, the energy levels are found to be
2 2
, ,= 2n l n lE k md , where the ,n lk are the spherical Bessel
function, ( )lj kr [24]. The effective value of d is the diam-
eter of the cage minus twice the hard core radius of the
molecule. The lowest energy levels are found to be 1.9,
4.4, 5.6, 7.4 K [18].
4. Conclusion
Studies of the nuclear spin relaxation times of molecules
adsorbed in mesoporous structures can provide direct non-
invasive measurements of the translational and rotational
dynamics of the molecules constrained to the pores of the
structures. The activation energies observed for both HD and
CH4 measurements appear to be in reasonably good agree-
ment with results reported from studies using other tech-
niques. The most unusual feature was the observation of
relatively sharp peaks in the relaxation times at low tempera-
tures for the translational energies. These peaks are close to
the energy values expected for the quantization of the trans-
lational motion for a particle in the pores, but further studies
are needed to verify this interpretation.
Acknowledgments
This research was supported in part by the National
Science Foundation through the award DMR-1303599. We
also gratefully acknowledge support from the electronics
and machine shops of the Department of Physics at the
University of Florida.
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1. Introduction
2. Experimental methods
3. Experimental observations
3.1. Adsorbed methane
3.2. HD on zeolite 13X and Z-MOF
4. Conclusion
Acknowledgments
|