64
3 Gas Hydrates
would expect the structurally hollow ice to be a poorer thermal conductor than
a “filled” clathrate hydrate. The thermal expansion coefficients of both sI and sII
hydrates increase with temperature and range from 10
−5 to 10
−4 K
−1 [1, 18, 29–36].
3.1.4 Mechanical Properties
Shimizu et al. measured the adiabatic elastic moduli, the bulk moduli, and the elastic
anisotropy of single-crystalline, sI-forming, methane hydrate as a function of pressure up to 600 MPa [37]. They found that the fully occupied methane hydrate has
slightly greater moduli than the 75% occupied methane hydrate. The values of the
elastic moduli depended on the crystallographic direction, due to the crystallographic
anisotropy, and they increased more or less linearly with the pressure. For example,
the bulk modulus increased from ≈8 GPa at 296 K and 20 MPa to ≈12 GPa at 296 K
and 600 MPa [37].
Helgerud et al. measured the compressional- and shear-wave velocity on
compacted polycrystalline sI-forming methane hydrate and sII-forming methane–
ethane mixed gas hydrate [38]. Although they did not provide the numerical values
of the moduli, they showed that the compressional- and shear-wave velocities of the
sII hydrate were similar to those of the sI hydrate [38]. This is in agreement with
Whaley’s finding earlier that the relative speed of the longitudinal sound wave in sI
and sII hydrates to be about 6% less than that of ice [39]. A somewhat smaller result
was obtained by Whiffen et al. who reported that the relative speed of the longitudinal
sound wave in sI hydrate to be about 12% less than that of ice [40]. Kiefte et al. found
that the acoustic velocity in sI hydrates decreased with increasing mass of the guest
and 3% to 24% smaller than that of ice (Ih) [41].
Shimizu et al. found that single-crystalline methane hydrate was slightly more
compressible than ice (Ih) at 296 K and in the pressure range of 20–600 MPa [37].
This is in contrast to the finding of Durham et al. who reported that polycrystalline
methane hydrate could be as much as 40 times stronger (creep resistant) under stress
than ice (Ih) in the range 260–287 K and 50–100 MPa [42].
3.1.5 Electromagnetic Properties
The dispersion relations of dielectric functions are the central electromagnetic properties of a given material that involve interactions between photons and electrons.
Unfortunately, dispersion relations have rarely been measured for clathrate hydrates.
A notable exception is for an sI-forming tri-methylene oxide hydrate over a range
of 10 Hz and 1 MHz [43]. Both the real part, ε
, and the imaginary part, ε
, of the
dielectric function ε complex ≡ ε
+ iε
showed strong temperature dependence over
the temperature range studied (between 1.8 K and 200 K) [43]. As for ε
at the zero
frequency limit, the dielectric constant was found to be ≈58 for both sI and sII,
3 Gas Hydrates
would expect the structurally hollow ice to be a poorer thermal conductor than
a “filled” clathrate hydrate. The thermal expansion coefficients of both sI and sII
hydrates increase with temperature and range from 10
−5 to 10
−4 K
−1 [1, 18, 29–36].
3.1.4 Mechanical Properties
Shimizu et al. measured the adiabatic elastic moduli, the bulk moduli, and the elastic
anisotropy of single-crystalline, sI-forming, methane hydrate as a function of pressure up to 600 MPa [37]. They found that the fully occupied methane hydrate has
slightly greater moduli than the 75% occupied methane hydrate. The values of the
elastic moduli depended on the crystallographic direction, due to the crystallographic
anisotropy, and they increased more or less linearly with the pressure. For example,
the bulk modulus increased from ≈8 GPa at 296 K and 20 MPa to ≈12 GPa at 296 K
and 600 MPa [37].
Helgerud et al. measured the compressional- and shear-wave velocity on
compacted polycrystalline sI-forming methane hydrate and sII-forming methane–
ethane mixed gas hydrate [38]. Although they did not provide the numerical values
of the moduli, they showed that the compressional- and shear-wave velocities of the
sII hydrate were similar to those of the sI hydrate [38]. This is in agreement with
Whaley’s finding earlier that the relative speed of the longitudinal sound wave in sI
and sII hydrates to be about 6% less than that of ice [39]. A somewhat smaller result
was obtained by Whiffen et al. who reported that the relative speed of the longitudinal
sound wave in sI hydrate to be about 12% less than that of ice [40]. Kiefte et al. found
that the acoustic velocity in sI hydrates decreased with increasing mass of the guest
and 3% to 24% smaller than that of ice (Ih) [41].
Shimizu et al. found that single-crystalline methane hydrate was slightly more
compressible than ice (Ih) at 296 K and in the pressure range of 20–600 MPa [37].
This is in contrast to the finding of Durham et al. who reported that polycrystalline
methane hydrate could be as much as 40 times stronger (creep resistant) under stress
than ice (Ih) in the range 260–287 K and 50–100 MPa [42].
3.1.5 Electromagnetic Properties
The dispersion relations of dielectric functions are the central electromagnetic properties of a given material that involve interactions between photons and electrons.
Unfortunately, dispersion relations have rarely been measured for clathrate hydrates.
A notable exception is for an sI-forming tri-methylene oxide hydrate over a range
of 10 Hz and 1 MHz [43]. Both the real part, ε
, and the imaginary part, ε
, of the
dielectric function ε complex ≡ ε
+ iε
showed strong temperature dependence over
the temperature range studied (between 1.8 K and 200 K) [43]. As for ε
at the zero
frequency limit, the dielectric constant was found to be ≈58 for both sI and sII,