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ISSN 1061-933X, Colloid Journal, 2020, Vol. 82, No. 2, pp. 180–187. © Pleiades Publishing, Ltd., 2020.
Russian Text © The Author(s), 2020, published in Kolloidnyi Zhurnal, 2020, Vol. 82, No. 2, pp. 223–230.
Molecular Dynamics Simulation of the Stability of Spherical
Nanoclusters of Methane and Carbon Dioxide Hydrates
A. A. Sizovaa, *, V. V. S izova, and E. N. Brodskayaa
aSt. Petersburg State University, St. Petersburg, 198504 Russia
*e-mail: shapovalovaaa@mail.ru
Received October 7, 2019; revised October 14, 2019; accepted October 17, 2019
Abstract—The stability of spherical nanoclusters of methane and carbon dioxide hydrates in the environment
of supercooled water has been studied by the molecular dynamics method under the isochoric and isobaric
conditions. The process of system melting has been considered within a temperature range of 180–280 K and
at pressures of 1, 50, and 100 atm (under isobaric conditions). It has been shown that clusters of CO2 hydrate
melt at temperatures lower than clusters of CH4 hydrate do. The difference between the melting temperatures
of the hydrates is about 40 K, which is explained by the higher solubility of carbon dioxide in water. The dif-
fusion coefficients calculated for water and the gases attest to different mechanisms of melting their hydrates.
The stability of the hydrates under the isochoric conditions appears to be lower than that under the isobaric
conditions. For simulation under isobaric conditions, changes in the pressure and the degree of carbon diox-
ide filling have no effect on the position of the range of melting of hydrate nanoclusters.
DOI: 10.1134/S1061933X2002012X
INTRODUCTION
Gas hydrates are nonstoichiometric compounds,
which consist of a crystalline water matrix formed by
hydrogen bonds, with the structure of the matrix being
stabilized by gas molecules. The gas is located in cavi-
ties, these being polyhedrons, with H2O molecules
being located in their lattice sites. The structure and
number of the cavities contained in a hydrate predeter-
mine its type and structure. For example, the unit cell
of a hydrate with the sI structure consists of two
dodecahedral (512) cavities, which are referred to as
“small” cavities, and six “large” tetradecahedral
(51262) cavities.
Among all gas hydrates, methane hydrates seem to
be most widely studied due to their prevalence in the
nature and the possibility of their use as a source of
fossil fuel. One of the approaches proposed for meth-
ane recovery from hydrate deposits is its replacement
by CO2 molecules with the concomitant solution of
the problem concerning the sequestration of excess
technogenic carbon dioxide [1]. This approach is fea-
sible, because, as has been experimentally shown, CO2
hydrate is more stable than CH4 hydrate under the
conditions of the replacement. Therewith, the tem-
perature difference for a fixed pressure is about 5 K,
while the difference in the equilibrium pressures is
nearly 20 atm at a given temperature [2]. However, the
direct replacement of methane by carbon dioxide in a
hydrate under the diffusion regime is unfeasible
because of the very low diffusion coefficients of the
gases. Moreover, the gas replacement is complicated
by the so-called “self-preservation” of hydrates, when
the crystalline phase occurs in a metastable state above
the equilibrium melting temperature under atmo-
spheric pressure. Therefore, a two-step procedure of
gas replacement is considered, which implies methane
hydrate dissociation into water and a gas phase fol-
lowed by carbon dioxide hydrate formation. Neverthe-
less, experimental data on such processes often appear
to be ambiguous and difficult to explain [3]. There-
fore, an important role in the study of each phase
transformation of gas hydrates, primarily, methane
and carbon dioxide hydrates, is played by the methods
of molecular simulation [4]. Great attention is focused
on the selection of force fields for the adequate repre-
sentation of the properties of hydrates. For example,
depending on a model employed for water, a substan-
tial scatter is observed in the values of the parameters
of phase transitions in gas hydrate systems [5–7]. In
the majority of works devoted to hydrate dissociation,
samples of bulk hydrates or hydrates with planar
boundaries are simulated; i.e., it is assumed that a sys-
tem is of macroscopic size (see, e.g., [8–11]). How-
ever, in both laboratory experiments and the nature,
hydrates are represented by semicrystalline systems
containing particles with different sizes, including
nanosized ones. In the latter case, the particle size
must substantially affect the phase state of a hydrate.
Few works [12–16] have been devoted to the simu-
lation of nanosized hydrates. The phenomenon of
self-preservation has been studied in detail by the
COLLOID JOURNAL Vol. 82 No. 2 2020
MOLECULAR DYNAMICS SIMULATION OF THE STABILITY 181
example of melting spherical nanoparticles of hydrates
in [14–16]. In [14], the phase transition temperature
was studied for two systems: an isolated gas hydrate
cluster surrounded with a thin ice shell and a bulk ice–
methane hydrate system. It has been shown that, in the
case of a nanoparticle, a thin ice shell cannot provide
the necessary growth of pressure in a hydrate; there-
fore, the stability of the nanoparticle is lower than that
in the case of a bulk system, in which conglomerates of
ice-coated hydrate crystals are formed. In [15], molec-
ular dynamics was used to simulate nanoclusters of
methane and krypton hydrates and determine their
melting temperatures on the basis of caloric curves.
The Lindeman criteria and the temperature depen-
dences of the diffusion coefficients of the system com-
ponents were found. It has been shown that nanoclus-
ters of hydrates with a radius of nearly 1.5 nm are more
stable than an analogous ice nanocluster: the melting
temperature is approximately 25 and 15 K higher for
methane and krypton hydrates, respectively. In turn,
the melting temperature of an ice nanocluster placed
into supercooled water has appeared to be almost
equal to the melting temperature of bulk ice. The anal-
ysis of variations in the mechanical state (local pres-
sure tensor) of nanoclusters of methane and krypton
hydrates [16] has shown that, at a low external pres-
sure, the main condition for an increased stability is
the existence of a gasproof water shell. Moreover, a
monolithic ice shell promotes the development of an
increased pressure in a hydrate, with this pressure sta-
bilizing its phase state.
Much less attention has been focused on nanohy-
drates of other gases, in particular, CO2.
The goal of this work was to compare the stabilities
of nanoclusters of CO2 and CH4 hydrates using results
of molecular dynamics calculations. For this purpose,
melting of spherical particles of these two hydrates in
the environment of supercooled water was simulated
within a wide temperature range. The melting tem-
perature was determined as the upper boundary of the
range of noticeable variations in the structural, trans-
port, and energy characteristics of a system being
heated.
SIMULATION DETAILS
The systems considered in this work contained a
nanosized cluster of a gas hydrate placed into super-
cooled liquid water. Nanoclusters of methane and car-
bon dioxide hydrates were prepared by cutting a spher-
ical particle 32 Å in diameter from bulk hydrates of the
sI structure (Fig. 1). Such a sample contained 99 gas
molecules and 588 water molecules under the condi-
tions of the complete filling. In the case of CO2
hydrate, the melting of a partly filled hydrate nano-
cluster was additionally studied. Carbon dioxide mol-
ecules occupied either 85 randomly chosen cavities or
only large cavities, while small cavities remained
empty. Spherical clusters of the hydrates were placed
into a cubic cell filled with supercooled water. Molec-
ular dynamics simulation was performed using the
GROMACS 2016.4 software package [17, 18] under
the isochoric (NVT ensemble) and isobaric (NpT
ensemble) conditions, thus making it possible to com-
pare the stabilities of the nanoclusters at different fixed
macroscopic parameters and reveal the effect of pres-
sure on the melting process.
To study the melting process, the system tempera-
ture was gradually increased from 180 K, at which a
cluster was, a fortiori, stable, to a temperature at which
the clusters were completely decomposed (in this
Fig. 1. Snapshots of methane (on the left) and carbon dioxide (on the right) hydrate nanoclusters before melting (180 K).
182
COLLOID JOURNAL Vol. 82 No. 2 2020
SIZOVA et al.
work, 280 K) with steps of 10 K. Three values of pres-
sure were used: 1, 50, and 100 atm. The temperature
and pressure were maintained constant using a Ber-
endsen thermostat and barostat with a relaxation time
of 1 ps. When performing the simulation in the NpT
ensemble, the average density of ambient water, which
depended on the preset pressure and temperature, was
determined. When the simulation was carried out
under the isothermal–isochoric conditions at all tem-
peratures, supercooled water had a constant density
equal to the density of water in a hydrate. The calcula-
tions were performed for 100–250 ns with a time step
of 1 fs. The characteristics of the systems were calcu-
lated within the equilibrium part of the trajectory with
a length of at least 30 ns (depending on the magnitude
of fluctuations). The establishment of stable equilib-
rium was confirmed by the absence of a drift in the
average value of the system potential energy.
The intermolecular interactions in a system were
described by the sum of the Lennard-Jones and Cou-
lomb potentials; the cutoff radius was 15 Å. The long-
range electrostatic interaction was taken into account
by the particle mesh Ewald (PME) method. The
OPLS-UA [19] and TraPPE [20] models were used for
methane and carbon dioxide, respectively. The
TIP4P/ice model [21] was chosen for water. This
model differs from the SPC/E model, which we used
previously [15], in a higher melting temperature close
to the experimental value. The cross-coupling interac-
tions were determined using the Lorenz–Berthelot
rule with the exception of parameter ε for the interac-
tion between the carbon atoms of CO2 and the oxygen
atoms of water. It was shown in [5] that its value must
be increased by a factor of 1.08 to correctly reproduce
the properties of bulk hydrates.
To determine the stability of nanoclusters of meth-
ane and carbon dioxide hydrates, the temperature
dependences were obtained for various characteristics
such as the radial distribution functions, diffusion
coefficients, and intermolecular interaction energies
of the gases. Taking into account the chosen interval
between neighboring temperature values, the error in
the determination of the melting point was nearly 5 K.
RESULTS AND DISCUSSION
It is known that, in contrast to bulk phases, melting
of small particles is a continuous process, which
occurs in some temperature range and is accompanied
by noticeable variations in all properties of a system.
The upper boundary of this range may be taken as the
characteristic value of the melting temperature. To
determine the melting points of hydrate nanoclusters
in the systems under investigation, the radial distribu-
tion functions (RDFs), diffusion coefficients of the
gases, and potential energy of the interaction between
the components of the systems were calculated at dif-
ferent temperatures.
Radial Distribution Functions
Methane hydrate decomposition upon heating is
evident from changes in the RDFs obtained by molec-
ular dynamics simulation. Figure 2a shows the meth-
ane–methane two-particle distribution functions cal-
culated in the NVT ensemble. At 200 K, distinctly
resolved high peaks are observed, which indicate the
existence of an ordered structure of methane located
in hydrate cavities. The distance between adjacent
methane molecules is about 6.5 Å, while the number
of such neighbors is 9.4. Analogous structural charac-
teristics were obtained at temperatures of 180, 210,
220, and 230 K. At 240 K, the intensities of the max-
ima are decreased, and the peaks are smoothed. It fol-
lows from Fig. 2 that the hydrate is completely decom-
posed upon the passage from 250 to 260 K. At the
same time, the amount of the adjacent neighbors in
the system decreases to 5.2 at 250 K and becomes
almost zero (0.2) at 260 K.
According to the C–O (methane–water) radial
distribution functions (Fig. 2b), the crystalline struc-
ture is completely destroyed at 260 K. However, it
should be noted that the intensity of the maxima
begins to decrease at a lower temperature (230 K). This
indicates that hydrate melting begins from the destroy-
ing of the water matrix, thereby promoting subsequent
escape of the gas from the cavities. The number of
water molecules in the first coordination sphere of
methane calculated from the C–O distribution func-
tion was equal to 18 and 2 before and after melting,
respectively. Thus the structural data indicate that,
under the isochoric conditions, methane hydrate
melts completely at 260 K.
The RDFs obtained under the isothermal–isobaric
conditions are qualitatively similar to those presented
above; however, the crystalline structure is, in this
case, completely destroyed upon an increase in the
temperature from 260 to 270 K at all three pressures (1,
50, and 100 atm). The number of adjacent neighbors
determined from the C–C and C–O RDFs in the NpT
ensemble coincides at a high accuracy with that
obtained under the isochoric conditions (the differ-
ence is no larger than 5%). Hence, at a fixed pressure,
methane hydrate melts at a temperature of 270 K,
which is 10 K higher than the value found under the
isochoric conditions.
The temperatures of the melting onset and the
complete decomposition of the nanocluster of carbon
dioxide hydrate were determined in a similar way.
Under the isochoric conditions, the peaks in the RDF
of the gas molecules (C–C) began to be smeared
already at 200 K, while the complete destruction was
observed at 220 K. Fot the simulation of carbon diox-
ide hydrate under the isobaric conditions, the crystal-
line structure disappeared in the C–C distribution
function at 230 K irrespective of the pressure (Fig. 3a).
As in the case of methane hydrate, the number of adja-
COLLOID JOURNAL Vol. 82 No. 2 2020
MOLECULAR DYNAMICS SIMULATION OF THE STABILITY 183
cent gas molecules was equal to nine and close to zero
(0.3 at 230 K) before and after melting, respectively.
In contrast to methane hydrate, the gas–water
(C‒O) RDFs exhibit a structural transition upon
melting in the same temperature range in which do the
C–C RDFs; i.e., the structures of water and carbon
dioxide are destroyed simultaneously. The number of
water molecules adjacent to CO2 varies in the same
manner as it does in the case of methane hydrate (17
and 2 before and after melting, respectively).
As is seen in Fig. 3, CO2 melts more abruptly than
does CH4 hydrate. This finding is confirmed by the
fact that the numbers of adjacent neighbors at pre-
melting temperatures are larger in the case of carbon
dioxide: 8 gas molecules and 15 water molecules at
230 K, while, for methane, they are 5 and 7 molecules,
respectively, at 260 K.
For the clusters of both gases, the melting tempera-
ture at a constant pressure appears to be higher than
that at a constant volume; i.e., the nanoclusters of
methane and carbon dioxide hydrates turn out to be
more stable under the isobaric conditions. According
to the obtained structural data, the difference between
the melting temperatures calculated in the NVT- and
NpT ensembles is 10 K for both hydrates. However, the
melting temperature appears to be insensitive to pres-
sure within the considered range (1–100 atm). Note
that the lower melting temperature of a carbon dioxide
cluster than that of a methane cluster contradicts to
the experimental data on the more stable state of bulk
carbon dioxide hydrates.
Fig. 2. Radial distribution functions (a) methane–meth-
ane (C–C) and (b) methane–water (C–O) under isocho-
ric conditions at different temperatures: (1) 200, (2) 250,
and (3) 260 K.
0
10
20
(а)
1
2.50.5 1.0 1.5 2.0
r, nm
RDF
2
3
0
10
30
20
(b)
1
2.50.5 1.0 1.5 2.0
r, n
m
RDF
2
3
Fig. 3. Radial distribution functions (a) СO2–CO2 (C–C)
and (b) СO2–H2O (C–O) under isobaric conditions at
different temperatures: (1) 210, (2) 220, and (3) 230 K.
0
10
20
(а)
1
2.50.5 1.0 1.5 2.0
r, n
m
RDF
2
3
0
10
20
(b)
1
2.50.5 1.0 1.5 2.0
r, nm
RDF
2
3
184
COLLOID JOURNAL Vol. 82 No. 2 2020
SIZOVA et al.
Self-Diffusion Coefficients
In addition to the structure, transport characteris-
tics are parameters sensitive to a phase state, with these
characteristics being represented in this work by diffu-
sion coefficients. Self-diffusion coefficients D were
calculated for molecules of the gases and water using
the Einstein relation for the time dependence of the
mean square displacements of the molecules.
Figure 4 shows the temperature dependences of the
diffusion coefficients for methane and water con-
tained in the hydrate under different conditions, i.e.,
at a constant pressure or volume. At 180–220 K, the
diffusion coefficients of the molecules are close to
zero; i.e., the hydrate structure remains preserved. As
the temperature is further elevated, the diffusion coef-
ficients begin to gradually grow, thereby indicating the
appearance of “mobile” molecules that have passed
from a hydrate into the environment, i.e., the crystal-
line structure begins to be destroyed. For both sub-
stances, the constancy of pressure corresponds to
lower values of diffusion coefficients. Therewith, the
diffusion coeff icient of water begins to grow at a lower
temperature and turns out to be higher than that of
methane. For example, under the isochoric condi-
tions, a noticeable increase in the diffusion coefficient
of H2O takes place already at 230–240 K, while for
methane, it is observed at 250 K (Fig. 4, curves 2, 4).
When simulating the system at a constant pressure of
50 atm, the mobility of molecules begins to increase at
higher temperatures: 240–250 K for water and 260 K
for methane (Fig. 4, curves 1, 3). Judging by the data
obtained, it may be assumed that methane hydrate
begins to melt at 250 and 260 K under the isochoric
and isobaric conditions, respectively.
Diffusion coefficients of carbon dioxide at differ-
ent temperatures are presented in Fig. 5. Mobility of
gas molecules increases at temperatures of 220 and
230 K at constant volume and pressure, respectively
(Fig. 5, curves 1, 3). For carbon dioxide hydrate at a
constant pressure, additional calculations of melting
were performed for a structure with incomplete filling,
when only 86% of the cavities in the hydrate were ini-
tially occupied with the gas (Fig. 5, curve 2). It is seen
that, below 230 K, the mobility of carbon dioxide mol-
ecules in the hydrate is independent of the degree of
filling of the cavities; however, at 240 K, the gas diffu-
sion coefficient in the partly filled hydrate becomes
noticeably higher than that in the case complete fill-
ing. Probably, the temperature of 240 K corresponds
to a liquid solution of carbon dioxide, and its concen-
tration in the case of initial partly filled hydrate is
lower than the concentration for the completely filled
hydrate. The decrease in the gas concentration may
explain the increase in its diffusion coefficient. How-
ever, a noticeable variation in the diffusion coefficient
with an increase in the temperature takes place in the
same temperature range for both distributions of mol-
ecules over the cavities (a random filling or the filling
of only large cavities). Thus, it can be seen that the
melting of the partly and completely filled hydrates
begins at the same temperature of nearly 230 K (Fig. 5,
curves 2, 3).
The behavior of water diffusion coefficient in this
system differs from that observed for methane hydrate:
its values are lower than those of carbon dioxide, and
its growth begins at a higher temperature (240 K). It
may be concluded that, in contrast to methane
Fig. 4. Temperature dependences of self-diffusion coeff i-
cients D: (1) methane, isobar (50 atm); (2) methane, iso-
chore; (3) water, isobar (50 atm); and (4) water, isochore.
0
15
10
5
20
1
260210 220 230 240 250
Т, К
D, 10–7 сm2/s
2
3
4
Fig. 5. Temperature dependences of self-diffusion coeffi-
cients D for (1–3) carbon dioxide and (4) water: (1) com-
plete occupancy, isochore; (2) incomplete occupancy
(large cavities), isobar (100 atm); (3) complete occupancy,
isobar (100 atm); and (4) complete occupancy, isobar
(100 atm).
3
0
9
6
1
240210 220 230
Т, К
D
, 10–7 сm2/s
2
3
4
COLLOID JOURNAL Vol. 82 No. 2 2020
MOLECULAR DYNAMICS SIMULATION OF THE STABILITY 185
hydrate, carbon dioxide hydrate begins to melt from
the escape of gas molecules from the hydrate followed
by decomposition of the water matrix. This indicates
that the decomposition mechanism of carbon dioxide
hydrate differs from that of methane hydrate.
Note that, in all systems, diffusion coefficients of
the gases and water obtained at different pressures
coincide with each other within the determination
error throughout the considered temperature range.
Energy Characteristics
Variations in the energy characteristics upon melt-
ing are illustrated by the temperature dependences of
potential energy E of the interaction between gas mol-
ecules for a constant pressure and a constant volume
(Fig. 6).
It should be noted that this characteristic differs
from the traditionally used caloric curve. This is due to
the fact that a nanosized sample of a hydrate is a small
part of a considered system, and variations in its
energy have a weak effect on the behavior of the entire
system energy.
Stronger interactions are observed between carbon
dioxide molecules primarily due to the existence of
electrostatic contribution. Upon melting, the inter-
molecular interaction weakens, while the potential
energy increases. Before and after the range of melt-
ing, the E(T) dependences exhibit plateaus that corre-
spond to the energies of the interaction between gas
molecules in the hydrate and the aqueous solution,
respectively. The melting of methane hydrate at a con-
stant volume or pressure (Fig. 6, curves 1, 3) is accom-
panied by a dramatic increase in the potential energy
at the same temperature (250 K). However, the pla-
teau is reached (the melting is completed) under the
conditions of a constant volume at a temperature
(260K) 10 K lower than it is at a constant pressure
(270 K).
A change in the external conditions has a notice-
able effect only on the energy of carbon dioxide
hydrate (Fig. 6, curves 2, 4). In the temperature
dependence of the energy, the temperature range that
corresponds to melting appears to be markedly nar-
rower than that for methane, as was noted above when
analyzing the RDFs. Under the isochoric conditions,
carbon dioxide hydrate begins to melt at 210 K (Fig. 6,
curve 4), while the potential energy of the CO2–CO2
interaction reaches the plateau at 220 K. In the NPT
ensemble (Fig. 6, cur ve 3), no transition temperature
range is observed, in which the hydrate has already
begun to degrade but has not yet been decomposed
completely; i.e., the CO2 hydrate melts completely at
230 K.
DISCUSSION
The comparison of the data on the three consid-
ered characteristics—RDFs, diffusion coefficients,
and intermolecular interaction energies—shows that
the temperature range of melting for a methane
hydrate nanocluster is 250–270 K, while for a carbon
dioxide hydrate nanocluster it is 220–230 K. As might
be expected, the values obtained for methane hydrate
cluster are lower than those for bulk hydrate [22];
however, they are substantially higher than those
obtained for the cluster studied in [15] using another
model of water (SPC/E), with this model being char-
acterized by a lower melting temperature.
However, the melting temperatures obtained for
carbon dioxide hydrate are not only noticeably lower
than those presented in the literature for the simula-
tion of the phase diagram of the bulk hydrate in terms
of the same molecular model [22], but also lower than
the corresponding values for methane nanohydrate.
This may probably be explained by a higher solubility
of carbon dioxide from a hydrate nanocluster due to its
larger specific surface area than the area of the planar
surface of the bulk hydrate, with this circumstance
leading to a lower stability as compared with methane
nanohydrate.
When comparing the results obtained for the iso-
choric and isobaric conditions, the latter seem to bet-
ter correspond to real experimental data and natural
conditions. The fixation of the system volume entails
ignorance of its thermal expansion upon heating and a
change in its density upon melting. Variations in the
volume upon heating may be determined under the
isobaric conditions. Figure 7 shows two isobars for the
Fig. 6. Potential energy E of interaction between gas mol-
ecules. Isobaric conditions (50 atm): (1) CH4–CH4 and
(2) CO2–CO2 and isochoric conditions: (3) CH4–CH4
and (4) CO2–CO2.
–80
–110
–20
–50
1
280200 240
Т, К
Е, kJ/mol
2
3
4
186
COLLOID JOURNAL Vol. 82 No. 2 2020
SIZOVA et al.
temperature dependence of the volume for a system
containing carbon dioxide nanohydrate. Temperature
elevation leads to an expansion of a system, the volume
of which reaches a maximum value at a temperature of
210–220 K; then, it dramatically decreases. Note that,
after melting, the system volume becomes smaller
than the initial one. The volume decreases because the
density of supercooled water is higher than the density
of a hydrate. However, since the hydrate cluster occu-
pies only a small fraction of the system volume, the
value of the reduction in the total volume appears to be
smaller than the difference between the densities of the
two phases. It is seen that the system volume before
melting is, in fact, independent of pressure. Pressure
affects the system volume after the structure of the
hydrate is destroyed. For example, the volume at 100
atm turns out to be smaller than that at 1 atm by nearly
0.8%, which is, in the order of magnitude, comparable
with the difference between water densities at corre-
sponding pressures (nearly 0.5%).
CONCLUSIONS
Computer simulation methods have been
employed to determine the temperature ranges of
melting for spherical nanoclusters of carbon dioxide
and methane hydrates. It has been shown that a cluster
of CO2 hydrate melts at 220 and 230 K under the iso-
choric and isobaric conditions, respectively. A spheri-
cal nanoparticle of methane hydrate is completely
decomposed at temperatures of 260 and 270 K (NVT
and NpT ensembles, respectively). Thus, the differ-
ence between the melting temperatures of the hydrates
is about 40 K.
The observed contradiction to the data on bulk
hydrates seems to be due to an increase in the solubil-
ity of CO2 from the nanohydrate surface as compared
with a bulk sample. This assumption is confirmed by
the behaviors of the diffusion coefficients of the gas
and water in this system. The results obtained—pri-
marily, the difference between the ratios of diffusion
coefficients for water and the gases upon melting of
the two hydrates—indicate different molecular mech-
anisms of their degradation upon heating.
The range of melting is actually independent of
pressure for the nanoclusters of the hydrates within a
pressure range of 1–100 atm.
The melting temperature of carbon dioxide nano-
hydrate has appeared to be insensitive to a decrease in
the occupancy of cavities to 86%.
FUNDING
This work was supported by the Russian Foundation for
Basic Research, project no. 18-03-00654 A.
CONFLICT OF INTEREST
The authors declare that they have no conflict of
interest.
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Fig. 7. System volumes V upon melting of carbon dioxide
hydrate in the NpT ensemble at different pressures: (1) 100
and (2) 1 atm.
180
190
185
1
180 210 240 270
Т, К
V, nm3
2
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Translated by A. Kirilin