Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances
The results of modeling of isotopic water mixture clusters in nitrogen and argon cryomatrices are presented. Earlier, our experimental studies of water mixture in cryomatrix have shown that changes in the concentration of analyte in matrix leads to a splitting of the absorption bands characteristi...
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Tychengulova, A. Aldiyarov, A. Drobyshev, A. 2017-12-31T13:50:01Z 2017-12-31T13:50:01Z 2015 Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances / A. Tychengulova, A. Aldiyarov, A. Drobyshev // Физика низких температур. — 2015. — Т. 41, № 6. — С. 582-587. — Бібліогр.: 18 назв. — англ. 0132-6414 PACS: 61.50.–f, 78.30–j, 68.35.Rh https://nasplib.isofts.kiev.ua/handle/123456789/127931 The results of modeling of isotopic water mixture clusters in nitrogen and argon cryomatrices are presented. Earlier, our experimental studies of water mixture in cryomatrix have shown that changes in the concentration of analyte in matrix leads to a splitting of the absorption bands characteristic frequencies of the molecules in the IR spectrum. Moreover the multiplicity of characteristic absorption bands in the IR spectrum remained unchanged during heating of the samples from the condensation temperature to the sublimation temperature of the matrix element. In order to find out what structure of clusters is responsible for the immutability of the absorption bands in the vibrational spectrum during thermal cycling of the samples, computer research of water molecules enclosed in nitrogen and argon cryomatrices by the molecular dynamics simulation was conducted. For this purpose, theoretical studies were carried out using computer software packages, that implement used by us semi empirical and ab initio molecular dynamics methods. As a result of the research, the data must be obtained are of theoretical interest for summarizing the physical and chemical properties of systems, consisting of water molecules, and their combination with inert gases for studying the properties of molecular crystals composed of small molecules. This work was financially supported by the Ministry of Education and Science of the Republic of Kazakhstan, grant IPS 31 with the state registration number № 0113RK00382. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур 10th International Conference on Cryocrystals and Quantum Crystals Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances Article published earlier |
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Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances |
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Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances Tychengulova, A. Aldiyarov, A. Drobyshev, A. 10th International Conference on Cryocrystals and Quantum Crystals |
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Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances |
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Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances |
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Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances |
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Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances |
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molecular dynamics simulation of thermodynamic and transport properties of h-bonded low-temperature substances |
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Tychengulova, A. Aldiyarov, A. Drobyshev, A. |
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Tychengulova, A. Aldiyarov, A. Drobyshev, A. |
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10th International Conference on Cryocrystals and Quantum Crystals |
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10th International Conference on Cryocrystals and Quantum Crystals |
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2015 |
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Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Article |
| description |
The results of modeling of isotopic water mixture clusters in nitrogen and argon cryomatrices are presented. Earlier,
our experimental studies of water mixture in cryomatrix have shown that changes in the concentration of
analyte in matrix leads to a splitting of the absorption bands characteristic frequencies of the molecules in the IR
spectrum. Moreover the multiplicity of characteristic absorption bands in the IR spectrum remained unchanged during
heating of the samples from the condensation temperature to the sublimation temperature of the matrix element.
In order to find out what structure of clusters is responsible for the immutability of the absorption bands in the vibrational
spectrum during thermal cycling of the samples, computer research of water molecules enclosed in nitrogen
and argon cryomatrices by the molecular dynamics simulation was conducted. For this purpose, theoretical
studies were carried out using computer software packages, that implement used by us semi empirical and ab initio
molecular dynamics methods. As a result of the research, the data must be obtained are of theoretical interest for
summarizing the physical and chemical properties of systems, consisting of water molecules, and their combination
with inert gases for studying the properties of molecular crystals composed of small molecules.
|
| issn |
0132-6414 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/127931 |
| citation_txt |
Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances / A. Tychengulova, A. Aldiyarov, A. Drobyshev // Физика низких температур. — 2015. — Т. 41, № 6. — С. 582-587. — Бібліогр.: 18 назв. — англ. |
| work_keys_str_mv |
AT tychengulovaa moleculardynamicssimulationofthermodynamicandtransportpropertiesofhbondedlowtemperaturesubstances AT aldiyarova moleculardynamicssimulationofthermodynamicandtransportpropertiesofhbondedlowtemperaturesubstances AT drobysheva moleculardynamicssimulationofthermodynamicandtransportpropertiesofhbondedlowtemperaturesubstances |
| first_indexed |
2025-11-25T21:02:35Z |
| last_indexed |
2025-11-25T21:02:35Z |
| _version_ |
1850543314980306944 |
| fulltext |
© A. Tychengulova, A. Aldiyarov, and A. Drobyshev, 2015
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6, pp. 582–587
Molecular dynamics simulation of thermodynamic and
transport properties of H-bonded low-temperature
substances
A. Tychengulova, A. Aldiyarov, and A. Drobyshev
Al-Farabi Kazakh National University, Almaty 050038, Kazakhstan
E-mail: Abdurakhman.Aldiyarov@kaznu.kz
Received January 8, 2015, published online April 23, 2015
The results of modeling of isotopic water mixture clusters in nitrogen and argon cryomatrices are presented. Ear-
lier, our experimental studies of water mixture in cryomatrix have shown that changes in the concentration of
analyte in matrix leads to a splitting of the absorption bands characteristic frequencies of the molecules in the IR
spectrum. Moreover the multiplicity of characteristic absorption bands in the IR spectrum remained unchanged dur-
ing heating of the samples from the condensation temperature to the sublimation temperature of the matrix element.
In order to find out what structure of clusters is responsible for the immutability of the absorption bands in the vi-
brational spectrum during thermal cycling of the samples, computer research of water molecules enclosed in nitro-
gen and argon cryomatrices by the molecular dynamics simulation was conducted. For this purpose, theoretical
studies were carried out using computer software packages, that implement used by us semi empirical and ab initio
molecular dynamics methods. As a result of the research, the data must be obtained are of theoretical interest for
summarizing the physical and chemical properties of systems, consisting of water molecules, and their combination
with inert gases for studying the properties of molecular crystals composed of small molecules.
PACS: 61.50.–f Crystal structure;
78.30–j Infrared and Raman spectra;
68.35.Rh Phase transitions and crytical phenomena.
Keywords: cryomatrix, polyaggregate, hydrogen bond, cryocondensate, molecular dynamics.
1. Introduction
“Water clusters”, groups of water molecules held to-
gether by hydrogen bonds, have been the subject of a num-
ber of intense experimental and theoretical investigations
[1–5] because of their importance in understanding of
cloud and ice formation, solution chemistry, and a large
number of biochemical processes. In this contribution, we
discuss the applicability of the methods of computational
chemistry for the theoretical study of ice crystal formation.
Besides, hydrogen bonds are very important for under-
standing molecular and crystal structures. Even though
they are not as strong as covalent bonds, they contribute
much to molecular mobility. All through the paper there
will be a lot talk about hydrogen bonding in water.
Studies of the properties of molecular crystals have a
special place in solid state physics. The relative simplicity
and understanding of Van der Waals forces that bind the
molecules in the lattice caused the interest that shows the
theory to molecular crystals. The substances selected by us
as objects of the study belong to the simplest Van der
Waals crystals. Due to the nature of their structure cryo-
crystals are closest to the models, considered by the theory,
and are ideal objects for studying the fundamental solid-
state physics [6].
The purpose of this paper is to obtain thermodynamic
and structural characteristics of cluster systems formed by
heavy water vapor and Ar and N2 gases are based on the
results of computer simulation. The infrared absorption
spectra for these systems will be calculated, as well as the
movement of molecules in clusters will be studied.
The remainder of this article is organized as follows.
Experimental procedures and results are described in
Sec. 2. In Sec. 3 we explain the computational model and
methods used to carry out the simulations and report their
results. The results are discussed and interpreted in Sec. 4
based on the spectra computed in our simulations.
mailto:Abdurakhman.Aldiyarov@kaznu.kz
Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 583
2. Experimental procedure
The basis of experimental method for obtaining the in-
formation about the state of isotopic water mixture mole-
cules in nitrogen cryomatrix lies on the analysis of absorp-
tion bands amplitude corresponding to vibrations of heavy
water molecules in unbound state. The measurements were
carried out using the setup the scheme and experimental
method of which is described in detail by the authors [7].
In this work we used the isotopic mixture of water with the
ratio (10% — H2O, 40% — D2O, 50% — HDO).
After film deposition at T = 16 K the IR spectrum were
measured, after which the substrate temperature is gradual-
ly increased until reaching the matrix evaporation tempera-
ture. In [8] the experimental data of the isotopic mixture of
water during heating were shown.
Figure 1 shows the spectrum of the cryocondensates of
isotopic water mixture in nitrogen cryomatrix, taken in
concentration of 1 to 10%, compared to 100% of the iso-
topic mixture into a solid state. In this frequency range
stretching vibrations of OH and OD bonds of heavy water,
and deformation vibrations of nonbounded water are ob-
served. Clear difference observed at spectra of isotopic
water mixture molecules isolated in nitrogen cryomatrix is
in presence of multiplicity of the absorption bands of vi-
brational spectrum compared with the spectrum of pure
mixture.
Appearance of multiplicity of the characteristic absorp-
tion bands of heavy water in nitrogen cryocondensates and
increasing of spectrum multiplicity with the decrease in the
concentration of water mixture in the matrix observed in
Fig. 1 are due to the formation in cryocondensates of
polyaggregates with different sizes. This issue is discussed
in detail in our previous studies [8]. According to [9] in
cryocondensates with the lowest concentration of the in-
vestigated substance in a matrix small clusters are formed
with the size of primarily dimers, trimers, etc.
Also in [10] shown that films with a higher concentra-
tion of water in nitrogen (10%) contribution of micro-
crystallites vibrations is very significant, while in the low
temperature the condensates with the least concentration of
the test mixture (1%), the contribution of small clusters
vibrations increases. This fact is confirmed in our studies,
in the case of consideration the isotopic water mixture as
the investigated substance, the spectrum of which is shown
in Fig. 2.
At a later stage, we investigated the resulting sample of
the cryocondensate film of heavy water in nitrogen
cryomatrix during heating to a temperature T = 34 K. The
results of this study are presented and analyzed in detail in
[8]. Thus becomes evident the absence of changes in the
spectrum of the vibrational frequencies of water in the ma-
trix as the temperature increases, i.e., the multiplicity of the
system is unchanged, until the value corresponding to the
matrix evaporation temperature. The question is why there
is no change in the structure of the crystallites and absence
of their associations into larger clusters. We have suggest-
ed that the observed phenomenon is due to formation by
water molecules in the matrix of stable clusters with cer-
tain size by hydrogen bonds between them. That is why it
was decided to test this hypothesis by computer modeling
of the system using molecular dynamics methods. The al-
gorithm and the results of the study are presented below.
3. Technique of molecular dynamics simulation
The intermolecular Van der Waals potentials between
atoms i and j on different molecules are taken as a sum of
Lennard-Jones (LJ) and electrostatic point charge interac-
tions. The Lennard-Jones ij and ij parameters are generally
taken from AMBER force field. The dynamics and hydro-
gen bonding calculations at each temperature and pressure
were studied with a standard algorithm of microcanonical
ensemble NVE (i.e., at constant number of particles, the
Fig. 1. (Color online) IR-spectra of isotopic water mixture in
nitrogen cryomatrix in frequencies interval 1200–4400 cm
–1
.
Fig. 2. (Color online) IR-spectra of isotopic water mixture in
nitrogen cryomatrix in frequencies interval 400–1400 cm
–1.
A. Tychengulova, A. Aldiyarov, and A. Drobyshev
584 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6
volume of the system and the total energy per particle) [11].
The researched system consisted of N = 3–20 of water mole-
cules in a cubic basic cell, the size of which varies from cal-
culation to calculation to set the required density.
Potential parameters or force fields are defined for each
molecule and constructed to take all important interactions
between molecules into account. Intermolecular pair-
potentials are expressed as:
12 6
( ) 4
i j ij ij
ij ij
ij ij ij
q q
U r
r r r
.
In order to avoid surface and finite-size effects, periodic
boundary conditions were used. Integration of the equa-
tions of motion was carried out on the basis of Verlet algo-
rithm with a time step of 0.1 fs. The water molecules used
to solvate a solute comes from Jorgensen’s Monte Carlo
equilibrated box of 215 molecules, described by the TIP3P
potential function [12]. This box is cubic and 18.70 Å on a
side. When the requested box fits into this, it is just carved
out of the basic Jorgensen box. When a bigger box (more
than 216 water molecules or perhaps an elongated box) is
required, then the basic 216 molecule box is duplicated to
create 3×3×3×216 water molecules in a box 56.10 Å on a
side and the required box is carved of this.
The integrated infrared band intensity for the kth fun-
damental is defined [12] as:
01
lnk
I
A d
CL I
,
where C is concentration (in moles liter
–1
), L is optical
path length (in cm), is wavenumber in cm
–1
, and I0 and
I, respectively, are the intensities of incident and transmit-
ted light. Assuming electric and mechanical harmonic, Ak
may be approximated by:
2
23000
a k
k
k
N g
A
Qc
,
where Na is the Avogadro number (mol
–1
), c is the light
velocity, gk is the degeneracy factor, and / kQ is the
dipole-moment derivative with respect to the kth normal
coordinate Qk.
Also, we performed first-principles, MD simulations of
H2On with n = 2, 4, 6 at two different temperatures by using
a pseudopotential, plane wave approach in conjunction with
a gradient corrected exchange-correlation functional Becke–
Lee–Yang–Parr (BLYP), as implemented in the density-
functional theory (DFT) package of the program. The choice
of the BLYP functional was motivated by its excellent per-
formance in describing the structural, energetic, and vibra-
tional properties of small water clusters, as compared to
higher level quantum chemical MP2 calculations [12]. Of
particular importance to this study is the ability of BLYP to
reproduce harmonic intermolecular vibrational frequencies
1000 cm
−1
. Atomic positions and electronic wave functions
were evolved at finite temperature with the Car–Parrinello
algorithm [13]. The electronic fictitious mass was set to a
value of 250 a.u., and equations of motion were integrated
with a time step of 5 a.u. Trajectories were initially equili-
brated by means of a Nose–Hoover thermostat [12] for
about 1–2 ps, followed by microcanonical runs of up to at
least 25 ps. Statistical averages were typically collected in
the last 20 ps of the simulation.
4. Results and discussion
Interactions between water molecules are far more
complicated than those between particles of simple liquids.
This complexity displays itself in the ability of H2O mole-
cules to form hydrogen bonds, making water an associated
liquid.
It is worth noting here that the use of simple water
models requires careful attitude to the results and their in-
terpretation, as well as perfect agreement with the experi-
mental data should not be expected in this case. However,
even with these limitations many important properties can
be found from the description of atomistic structure and
thermodynamics using MD methods, especially if the tra-
jectories of atoms are considered to obtain the information
on physical mechanisms behind experimentally observed
phenomena.
Clusters formed by D2O molecules are more stable and
resistant in comparison with clusters of water due to the
deuterium isotope effects caused by twice heavier mass of
deuterium. Furthermore D2O structure is similar to the
structure of water molecules with only one difference in
the lengths of covalent bonds. These effects result in the
fact that the hydrogen bonds formed by deuterium atoms
Fig. 3. (Color online) Cluster formation between heavy water
molecules through the hydrogen bonds [14].
Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 585
vary in strength and energy of hydrogen bonds in the nor-
mal water. In general, many authors noted that the isotope
effects stabilize the hydrogen bonds with deuterium, which
ultimately leads to the formation of stable associates of
D2O molecules [14].
As shown by computer modeling, the clusters are able
to interact with one another through the outer surfaces ex-
posed to hydrogen bonds (Fig. 3). Combined, they can
form a more complicated structure of from 5 to 20 or more
molecules of H2O. In clusters through cooperative interac-
tions between hydrogen bonds can occur proton migration
to the relay mechanism, leading to proton delocalization
within the cluster.
Computer modeling using molecular dynamics method
designed the structure and energy of water clusters. For
structures with the lowest energy the dependence of energy
on the clusters temperature are obtained and dependence of
the heat capacity and vibrational energy are identified.
Extensive ab initio calculations have been performed
using the 6–31 G basis sets for several possible structures
of water clusters. It is found that the most stable geome-
tries arise from a fusion of pentameric rings (Fig. 4).
Figure 5 shows the total potential energy during the
time of MD-simulation for the system of 20 heavy water
molecules. We can observe four exact stages in the con-
densation process: (1) a long period with relatively con-
stant potential energy (for about t = 15 ns); (2) a very short
period with slowly decreasing potential energy; (3) a peri-
od with rapid decrease of the potential energy; and (4) a
final period during which the potential energy remains
relatively constant and we can say, that the structure of ice
at this stage fully forms. The fact that the system explores
the overall relatively flat potential energy landscape for a
considerable time before entering the fast growing period
agrees with the predictions of basic nucleation theory [12].
Table 1 lists the scaled frequencies with maximum in-
tensities for some of these clusters along with the frequen-
cies of a single water molecule. The H–O–H angle defor-
mation frequency is observed to generally increase on
cluster formation. The O–H stretching frequencies, on the
other hand, generally decrease with increasing cluster size.
Also, it is noticed from Table 1 that the intensities of all
these vibrations are enhanced on cluster formation.
2ln ln
ln , ,B B B
Q Q
S k T k Q U k T
T T
, lnB
U
C F H TS k T Q
T
v .
where S is the entropy, U is the internal energy, Cv the
constant volume heat capacity, F is the Helmholtz free
energy, and kB the Boltzmann constant. In the harmonic
approximation, one approximates the normal modes of the
system to be a set of 3N harmonic oscillators, so that the
partition function Q can be expressed in term of the parti-
tion function qi for the individual modes [15]. For a con-
tinuous distribution of normal modes, the partition function
Q can be shown to be related to DOS( ) by [15]:
Fig. 4. (Color online) Water pentamers.
Fig. 5. The total potential energies of the instantaneous structures
in the trajectory for 20 molecules after quenching from T = 280 K
to 16 K.
Fig. 6. Linear vibrational absorption spectrum of ice formed by
20 molecules at Tc = 16 K calculated using the PM3 method.
Three intramolecular modes are preserved in ice, the bending
vibration and the overlapped symmetric and asymmetric stretch-
ing vibrations and one intermolecular mode (librations).
A. Tychengulova, A. Aldiyarov, and A. Drobyshev
586 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6
0
ln DOS( ) ( )Q W d ,
where W( ) is the relevant weighting function. Here, the
DOS( ) is obtained from the Fourier transform of the
atomic velocity autocorrelation functions
3
11
1
DOS ( ) li (m )
2
( )
N
k k
j j j
kj
m t t
kT
t ,
where ( ) ( )k k
j jt t t is the kth component of the veloci-
ty autocorrelation function of atom j at time t. Physically,
DOS( ) represents the density of normal modes of the
system at frequency .
We can observe that the dependence between log P and
Cv is linear as predicted by the theory:
( )
dp r
dT T V V
,
( )
dp r
pdT pT V V
,
2
log
r
p dT C
RT
v .
The assignment of the absorption bands at Fig. 6 around
= 3310, 1600 and 800 cm
–1
, respectively, to the stretch-
ing, bending and libration vibrations and is not in doubt.
We started our simulations from the known ground
state structures for the dimer and the tetramer cyclic. At
our BLYP level of theory, the ring structure (Fig. 4) has
the lowest energy among other degenerate geometries. The
obtained binding energies of the dimer, pentamer, and
hexamer ring, calculated after full relaxation of the atomic
positions without inclusion of quantum effects, are 0.09,
0.27, and 0.30 eV per molecule, respectively [16–18].
Calculations also showed that due to the ability of water
molecules to form hydrogen bonds this system has a great
variety of structures with substantially different binding
energy and heat capacity. Most stable ring structures
among them is pentamer ring structure shown in Fig. 4,
which has only one proton molecules involved in the for-
mation of hydrogen bonds. Orientation of such clusters in
cryomatrix of nitrogen and argon is shown at Fig. 7.
5. Conclusions
Experimentally shown that in isotopic water mixture in
nitrogen and argon matrices multiplicity of absorption
bands appears in the IR spectra of the samples with a de-
crease in their concentration, which, in our opinion, is due
Table 1. Vibrational frequencies calculated at program for (H2O)n
Structure code Scaled frequency, cm
–1
Intensity, arb. units Type
H2O
1770
4153
65
204
Bending
Stretching
(H2O)3
862.18
1622.37
2422
3701
93.72
55.4
944
151.6
Librations
Bending
Combination (bending+libration)
Stretching
(H2O)8
845.9
1637
3662
58.5
33.02
234.03
Librations
Bending
Stretching
(H2O)10
842
1664
2045
3663
103.79
236.15
573.02
438.2
Librations
Bending
Combination (bending+libration)
Stretching
(H2O)11
846
1688
3660
105.7905
50.22
260.23
Librations
Bending
Stretching
Table 2. Thermodynamic parameters of water clusters with different number of molecules at 16 K
Simulation type Number of molecules in cluster T, K log P V, 10
–10
m
3
S, kJ/(mol·K) Fvib, kJ/mol Cv, kJ/mol
NVE 3 16 –2.01 539.94 0.061 513.3 0.167
NVE 5 16 –4.09 778.65 0.15 920.88 0.202
NVE 8 16 –5.69 906.86 0.639 1115.4 0.488
NVE 10 16 –7.68 1212.17 0.9 1557 1.116
NVE 20 16 –8.19 2326.64 1.364 2253.3 1.205
Molecular dynamics simulation of thermodynamic and transport properties of H-bonded low-temperature substances
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 6 587
to the formation of small clusters of isotopic water mixture
molecules (dimers, trimers, etc). Computer model of this
system has shown that the formation of the cluster struc-
ture occurs at the time of condensation mixture. Calcula-
tion of change in the total energy of the system in time
confirms the assumption of the model. According to the
results of molecular dynamics calculations the following
conclusions can be formulated.
1. Analysis of the research results showed that the change
of crystal structure of the matrix element occurring in heat-
ing process of the sample from the condensation temperature
Tc = 16 K to the sublimation temperature of the matrix mol-
ecules do not affect the multiplicity of absorption bands at
characteristic frequencies of water molecules.
2. The vibrational spectrum obtained by calculation of
the sample’s computer model also reveals the presence of
characteristic absorption bands of free OH-bonds in water
molecules at cryomatrix.
3. Using the molecular dynamics method it has been
found that water molecules isolated in nitrogen, argon
cryomatrices at Tc = 16 K, form nanoclusters with stable
structure. Among them, the most stable structure is a pen-
tamer with the form of pentagon, and it was noted that in-
creasing the concentration of the mixture of molecules
(n ≥ 20) leads to the formation of two-dimensional penta-
gons.
This work was financially supported by the Ministry of
Education and Science of the Republic of Kazakhstan, grant
IPS 31 with the state registration number № 0113RK00382.
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Fig. 7. (Color online) Pentameric rings of heavy water in
cryomatrices of nitrogen (a) and argon (b).
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