Isobaric-isothermal molecular dynamics computer simulations of the properties of water-1,2-dimethoxyethane model mixtures
Isothermal-isobaric molecular dynamics simulations have been performed to examine a broad set of properties of the model water-1,2-dimethoxyethane (DME) mixture as a function of composition. The SPC-E and TIP4PEw water models and the modified TraPPE model for DME were applied. Our principal focus w...
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Інститут фізики конденсованих систем НАН України
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irk-123456789-1570102019-06-20T01:27:19Z Isobaric-isothermal molecular dynamics computer simulations of the properties of water-1,2-dimethoxyethane model mixtures Gujt, J. Dominguez, H. Sokolowski, S. Pizio, O. Isothermal-isobaric molecular dynamics simulations have been performed to examine a broad set of properties of the model water-1,2-dimethoxyethane (DME) mixture as a function of composition. The SPC-E and TIP4PEw water models and the modified TraPPE model for DME were applied. Our principal focus was to explore the trends of behaviour of the structural properties in terms of the radial distribution functions, coordination numbers and number of hydrogen bonds between molecules of different species, and of conformations of DME molecules. Thermodynamic properties, such as density, molar volume, enthalpy of mixing and heat capacity at constant pressure have been examined. Finally, the self-diffusion coefficients of species and the dielectric constant of the system were calculated and analyzed. Для того, щоб дослiдити широкий набiр властивостей модельних сумiшей вода-1,2-диметоксиетан (DME) в залежностi вiд концентрацiї, проведено комп’ютерне моделювання методом молекулярної динамiки в iзобарично-iзотермiчному ансамблi. Для води застосовано моделi SPC-E i TIP4P-Ew, а для DME — модифiковану модель TraPPE. Нашим основним завданням було дослiдити тенденцiю поведiнки структурних властивостей в термiнах радiальних функцiй розподiлу, координацiйних чисел та чисел водневих зв’язкiв мiж молекулами рiзних сортiв, а також конформацiї молекул DME. Вивчено термодинамiчнi властивостi, такi як густина, молярний об’єм, ентальпiя змiшування i питома теплоємнiсть при постiйному тиску. Накiнець, обчислено i проаналiзовано коефiцiєнти самодифузiї сортiв i дiелектричну сталу системи. 2017 Article Isobaric-isothermal molecular dynamics computer simulations of the properties of water-1,2-dimethoxyethane model mixtures / J. Gujt, H. Dominguez, S. Sokolowski, O. Pizio // Condensed Matter Physics. — 2017. — Т. 20, № 3. — С. 33603: 1–14. — Бібліогр.: 66 назв. — англ. 1607-324X PACS: 61.20.-p, 61.20-Gy, 61.20.Ja, 65.20.+w DOI:10.5488/CMP.20.33603 arXiv:1710.01204 http://dspace.nbuv.gov.ua/handle/123456789/157010 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Isothermal-isobaric molecular dynamics simulations have been performed to examine a broad set of properties
of the model water-1,2-dimethoxyethane (DME) mixture as a function of composition. The SPC-E and TIP4PEw water models and the modified TraPPE model for DME were applied. Our principal focus was to explore
the trends of behaviour of the structural properties in terms of the radial distribution functions, coordination
numbers and number of hydrogen bonds between molecules of different species, and of conformations of DME
molecules. Thermodynamic properties, such as density, molar volume, enthalpy of mixing and heat capacity
at constant pressure have been examined. Finally, the self-diffusion coefficients of species and the dielectric
constant of the system were calculated and analyzed. |
| format |
Article |
| author |
Gujt, J. Dominguez, H. Sokolowski, S. Pizio, O. |
| spellingShingle |
Gujt, J. Dominguez, H. Sokolowski, S. Pizio, O. Isobaric-isothermal molecular dynamics computer simulations of the properties of water-1,2-dimethoxyethane model mixtures Condensed Matter Physics |
| author_facet |
Gujt, J. Dominguez, H. Sokolowski, S. Pizio, O. |
| author_sort |
Gujt, J. |
| title |
Isobaric-isothermal molecular dynamics computer simulations of the properties of water-1,2-dimethoxyethane model mixtures |
| title_short |
Isobaric-isothermal molecular dynamics computer simulations of the properties of water-1,2-dimethoxyethane model mixtures |
| title_full |
Isobaric-isothermal molecular dynamics computer simulations of the properties of water-1,2-dimethoxyethane model mixtures |
| title_fullStr |
Isobaric-isothermal molecular dynamics computer simulations of the properties of water-1,2-dimethoxyethane model mixtures |
| title_full_unstemmed |
Isobaric-isothermal molecular dynamics computer simulations of the properties of water-1,2-dimethoxyethane model mixtures |
| title_sort |
isobaric-isothermal molecular dynamics computer simulations of the properties of water-1,2-dimethoxyethane model mixtures |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/157010 |
| citation_txt |
Isobaric-isothermal molecular dynamics computer simulations of the properties of water-1,2-dimethoxyethane model mixtures / J. Gujt, H. Dominguez, S. Sokolowski, O. Pizio // Condensed Matter Physics. — 2017. — Т. 20, № 3. — С. 33603: 1–14. — Бібліогр.: 66 назв. — англ. |
| series |
Condensed Matter Physics |
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AT gujtj isobaricisothermalmoleculardynamicscomputersimulationsofthepropertiesofwater12dimethoxyethanemodelmixtures AT dominguezh isobaricisothermalmoleculardynamicscomputersimulationsofthepropertiesofwater12dimethoxyethanemodelmixtures AT sokolowskis isobaricisothermalmoleculardynamicscomputersimulationsofthepropertiesofwater12dimethoxyethanemodelmixtures AT pizioo isobaricisothermalmoleculardynamicscomputersimulationsofthepropertiesofwater12dimethoxyethanemodelmixtures |
| first_indexed |
2025-07-14T09:21:27Z |
| last_indexed |
2025-07-14T09:21:27Z |
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1837613593457065984 |
| fulltext |
Condensed Matter Physics, 2017, Vol. 20, No 3, 33603: 1–14
DOI: 10.5488/CMP.20.33603
http://www.icmp.lviv.ua/journal
Isobaric-isothermal molecular dynamics computer
simulations of the properties of
water-1,2-dimethoxyethane model mixtures
J. Gujt1, H. Dominguez2, S. Sokolowski3, O. Pizio2∗
1 Chair of Theoretical Chemistry, Faculty of Chemistry, University of Duisburg-Essen, D-45141 Essen, Germany
2 Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Circuito Exterior,
04510, Cd. de México, México
3 Department for the Modelling of Physico-Chemical Processes, Maria Curie-Sklodowska University,
Lublin 20-614, Poland
Received May 8, 2017, in final form August 4, 2017
Isothermal-isobaric molecular dynamics simulations have been performed to examine a broad set of properties
of the model water-1,2-dimethoxyethane (DME) mixture as a function of composition. The SPC-E and TIP4P-
Ew water models and the modified TraPPE model for DME were applied. Our principal focus was to explore
the trends of behaviour of the structural properties in terms of the radial distribution functions, coordination
numbers and number of hydrogen bonds between molecules of different species, and of conformations of DME
molecules. Thermodynamic properties, such as density, molar volume, enthalpy of mixing and heat capacity
at constant pressure have been examined. Finally, the self-diffusion coefficients of species and the dielectric
constant of the system were calculated and analyzed.
Key words: water-DME mixtures, thermodynamic properties, self-diffusion coefficient, dielectric constant,
molecular dynamics
PACS: 61.20.-p, 61.20-Gy, 61.20.Ja, 65.20.+w
1. Introduction
It is our honour to dedicate this manuscript to the memory of an extraordinary scientist and extraor-
dinary person Jean-Pierre Badiali. One of us (O.P.), in particular, would like to appreciate friendship,
scientific and non-scientific discussions with Jean-Pierre during his visits in Ukraine and Mexico in past
decades. J.-P. Badiali has made important contributions in the area of theoretical electrochemistry and
one of his interests was in the properties of electrolyte solutions that involve combined solvents with
water and organic liquid components [1, 2]. Our present contribution is on this topic.
Various experimental techniques have been applied to several water-organic solvent mixtures for
specific purposes. As a result, numerous valuable experimental data have been accumulated. Still, even for
most popular systems of experimental interest such as water-alcohols, water-dimethylsulfoxide (DMSO),
water-amides, these studies have not been entirely comprehensive. Consequently, computer simulations,
most frequently the molecular dynamics studies, have been performed aiming at explaining experimental
findings and accumulation of data for the properties difficult or impossible to access in a laboratory.
Moreover, computer simulations permit to discern different factors contributing to a given result and can
provide a profound understanding of the trends of the behaviour of the properties of interest.
For specific purposes of our project, it is worth mentioning that molecular dynamics computer
simulations have been applied to mixtures of water with different organic solvents in a large number
∗On sabbatical leave from Instituto de Quimica de la UNAM. Corresponding author: oapizio@gmail.com.
This work is licensed under a Creative Commons Attribution 4.0 International License . Further distribution
of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
33603-1
https://doi.org/10.5488/CMP.20.33603
http://www.icmp.lviv.ua/journal
http://creativecommons.org/licenses/by/4.0/
J. Gujt, H. Dominguez, S. Sokolowski, O. Pizio
of works. We cite only some of them, just to provide the reader a taste of the objectives and principal
results for a few selected co-solvents. Namely, water mixed with different alcohols was studied in, e.g.,
[3–10], see references therein as well. On the other hand, liquid mixtures of water with dimethylsulfoxide
(DMSO) have been explored in [11–26]. Less attention has been paid to the exploration of the behaviour
of water-dymethylformamide (DMF) mixtures [27–33].
Finally, liquid mixtures of water with 1,2-dimethoxyetane (DME or monoglyme) were studied by
molecular dynamics computer simulations in, e.g., [34–37]. Meanwhile, DMSO and DMF are widely
used as solvents and reaction media in laboratory studies, the DME molecule is of interest as it is the
smallest element of the polyoxyethylene (POE), the water soluble polymer with various applications in
biomedicine. The hydrophilic and hydrophobic groups are combined in the DME molecular structure of
the form CH3-O-CH2-CH2-O-CH3, the intra- and intermolecular interactions are such that the DME is
highly soluble in water and in other solvents. Significant conformational changes of the intramolecular
structure depend on the co-solvent and are of interest to explore in the perspective of other chemical and
biochemical systems.
In close similarity to various previous studies, this work is performed in the framework of isobaric-
isothermalmolecular dynamics computer simulations. The structure of water-DMEmixtures on composi-
tion is explored in terms of different descriptors, namely the radial distribution functions and coordination
numbers, hydrogen bonding statistics and population of most abundant conformations of DME species.
Thermodynamic aspects of the behaviour of mixtures in question are discussed in terms of mixing prop-
erties. Insights into the dynamic properties are obtained by exploring the mean square displacements as a
function of time and the resulting self-diffusion coefficients of species. Finally, we discuss the behaviour
of the dielectric constant of the solutions upon changes in the solvent composition. Our study is restricted
to room temperature and ambient pressure (1 bar), only the chemical composition of the mixed solvent
represent the explored variable. Wider insights into thermodynamic properties, analyses of an broad set
of dynamic and dielectric properties, would require additional work.
2. Model and simulation details
Our calculations have been performed in the isothermal-isobaric (NPT) ensemble at 1 bar, and at
a temperature of 298.15 K. We used the GROMACS package [38] version 4.6.5. Solely the modified
TraPPE united atom model (TraPPE-UA) for DME [35] was used in our calculations. It consists of six
interaction sites (CH3, O, CH2, CH2, O, CH3). All the interaction parameters (charges, σ and ε for
Lennard-Jones interactions), harmonic bonds lengths, bond strengths, bend and torsional angles were
taken from the table 1 of [35]. Most important is that the model is perfectly well defined. In this aspect,
we would like to repeat the comment by Fischer et al. [35] “we did not try to reproduce their data, because
the employed force field parameters they used are not clearly indicated” referring to the model of Bedrov
et al. [36, 39]. On the other hand, we have failed to reproduce the data for the DME united atom type
model given in [37] for the reason just mentioned and due to misprints in table 1 of this article.
For water in the present study, the SPC-E model [40] and the TIP4P-Ew model [41] were used.
The Lorentz-Berthelot combination rules for diameters and energies were used to determine the cross
parameters. Nevertheless, we checked the effect of a combination rule on mixture density as function
of composition by applying the geometric combination rule (rule 3 in GROMACS nomenclature).
The nonbonded interactions were cut off at 1.59 nm, similar to [37], and the long-range electrostatic
interactions were handled by the particle mesh Ewald method implemented in the GROMACS software
package (fourth order, Fourier spacing equal to 0.12). The van der Waals tail correction terms to the
energy and pressure were taken into account. In order to maintain the geometry of the water and DME
molecules, the LINCS algorithm was used.
For each system, a periodic cubic simulation box was set up. The GROMACS genbox tool was
employed to randomly place all particles into the simulation box. The total number of molecules was
kept fixed at 3000. The composition of the mixture is described by the mole fraction of DME molecules,
Xdme, Xdme = Ndme/(Ndme + Nw).
To remove possible overlaps of particles introduced by the procedure of preparation of the initial
configuration, each system underwent energy minimization using the steepest descent algorithm imple-
33603-2
Water-DME properties from molecular dynamics simulations
mented in the GROMACS package. Minimization was followed by a 50 ps NPT equilibration run at
298.15 K and 1 bar using a timestep of 0.25 fs. We used the Berendsen thermostat and barostat with
τT = 1 ps and τP = 1 ps during equilibration. Constant value of 4.5 · 10−5 bar−1 for the compressibility
of the mixtures was employed.
The V-rescale thermostat and Parrinello-Rahman barostat with τT = 0.5 ps and τP = 2.0 ps and the
time step 2 fs were used during production runs. To test this thermostat and barostat, we have obtained
88.5 J/mol·K for the heat capacity of the SPC/E model. This value is close to 86.6 J/mol·K reported by
Vega et al. [42] (experimental result is 75.3 J/mol·K). On the other hand, we obtained 191.2 J/mol·K for the
heat capacity of DME, the experimental value reported by Trejo et al. [43] is 191.14 J/mol·K. Moreover,
the DME molar volume coming out from our calculations is 105.2 cm3/mol favourably comparing to
the experimental result 104.54 cm3/mol. Berendsen type control of temperature and pressure is not
satisfactory in this aspect.
Statistics for each mole fraction for some of the properties were collected over several 10 ns NPT
runs, each started from the last configuration of the preceding run. The total trajectory was not shorter
than 60 ns. Actually, the heat capacity and the dielectric constant are the most demanding properties.
3. Results and discussion
3.1. Density and mixing properties
To begin with, we would like to discuss the dependence of density of the water-DME mixture as
function of its composition. Previous comparisons, see figure 5 of [35], were made at T = 318 K using
TIP4P-Ew water model and several models for DME. It has been concluded that the combination of
TIP4P-Ew with two all-atom type models [44] performs worse than the the combination of TIP4P-Ew
with all-atom type model of [39] and the united atommodified TraPPEmodel of [35], in comparison with
the experimental data from [45]. On the other hand, a comparison of the theoretical and experimental
data given in figure 1 of [37] again refers to T = 318 K, but involves the SPC model of water [46]. The
quality of theoretical predictions is satisfactory.
Results of our calculations at T = 298.15 K are given in two panels, (a) and (b), of figure 1. In order
to perform comparisons, we have used three sets of experimental data, namely from [45, 47, 48]. From
the simulation data in panel (a) we learn that the theoretical curves slightly overestimate the density in
water-rich region comparing with the results of [45, 47] and slightly underestimate the density in the
DME-rich region, but this discrepancy is in fact rather small. Both models, i.e., the SPC-E and TIP4P-Ew,
are equally good. In addition, the application of geometric combining rule does not yield improvement
of the dependence of density on composition. It can be seen that the application of another DME model
in combination with the SPC water model (the data were compiled from table IIS of [37]) yields less
accurate results.
It is of interest to explore the accuracy of performance of the models by studying deviations from
the ideal type behaviour of different properties. One test for the species modelling is illustrated by the
calculations of the excess mixing density, ∆ρmix = ρ − (1 − Xdme)ρwater − Xdmeρdme (similar type of an
expression is used below to evaluate other mixing properties).
Our results are shown in panel (c) of figure 1. According to the experimental data of [45, 47], negative
deviation from the ideal type of mixing is observed in the entire range of composition whereas a weakly
pronounced positive deviation in the water-rich region comes out from the experimental data of [48]. The
simulation curves yield a reasonable description of∆ρ(Xdme) behaviour. The SPC-Ewater-DMEmodel is
closer to the experimental predictions, comparing to the TIP4P-Ew one. The most pronounced deviation
is observed in the interval of compositions between 0.5 and 0.6 whereas the experimental predictions of
[45, 47] show a maximum deviation from the ideal type of behaviour of this property at Xdme ≈ 0.45.
It is worth mentioning that for mixtures of water with methanol, ethanol and 1-propanol, as well as for
water-DMSO mixtures, ∆ρmix is positive in the entire chemical composition range, see, e.g., figure 2 of
[3] and figure 1 of [26], respectively. In the present system, the behavior of ∆ρmix is different due to the
intrinsic shape of the DMF molecule and due to the way these molecules accommodate one another.
33603-3
J. Gujt, H. Dominguez, S. Sokolowski, O. Pizio
0 0.2 0.4 0.6 0.8
X
dme
850
900
950
1000
ρ
(k
g
/m
3
)
Ref. [46]
Ref. [44]
Ref. [47]
SPC-E
TIP4P-Ew
a
0 0.2 0.4 0.6 0.8
X
dme
850
900
950
1000ρ (kg/m3
)
SPC - DME (Ref. [36])
SPC-E / CR3
TIP4P-EW / CR2
SPC-E / CR2
b
0 0.2 0.4 0.6 0.8 1
X
dme
-30
-20
-10
0
∆
ρ
m
ix
(
k
g
/m
3
)
Ref. [46]
Ref. [44]
Ref. [47]
TIP4P-Ew
SPC-E
DME - Modified TraPPE
c
Figure 1. (Color online) Panel (a): Composition dependence of the density of water-DME mixtures from
constant pressure-constant temperature simulations (T = 298.15 K, P = 1 bar) in comparison with the
experimental data from [45, 47, 48]. Panel (b): Simulation results for different models and from different
combination rules. Panel (c): Excess mixing density on composition.
Insights into mixing of species in the mixtures upon composition are commonly discussed by in-
specting a set of results given in figures 2 and 3. Namely, in figure 2 (a) we present our results for the
mixing volume for two models for water combined with the modified TraPPE model for DME. They
are compared with the experimental results from [48]. Both sets of theoretical results rather well agree
with experimental data. In particular, the simulations predict the magnitude of volume contraction and
the position of a minimum of ∆Vmix(Xdme) at Xdme ≈ 0.3. On the other hand, the energetic aspects of
mixing at a constant pressure are given by the excess mixing enthalpy, panel (b) of figure 2. Two versions
for water-DME models predict maximal mixing trends around Xdme ≈ 0.25, i.e., almost at the same
composition as the excess mixing volume. Unfortunately, we did not find experimental data to evaluate
the precision of the simulation results.
Thermodynamic aspects of mixing can be interpreted in terms of the behaviour of molar heat capacity.
This property was not discussed in previous publications on water-DME mixtures. The dependence of
molar heat capacity on the composition coming from our simulations is shown in panel (a) of figure 3.
The starting point for pure water and the final point for pure DME of the curve agree rather well with
experimental predictions as we have already mentioned in the previous section. Interestingly, the results
were extracted just using GROMACS software without taking into account the quantum corrections. The
only interesting observation is that the heat capacity grows faster with Xdme in the water-rich region and
then starting from Xdme ≈ 0.3 it changes almost linearly with an increasing concentration of organic
species. On the other hand, the excess mixing molar heat capacity exhibits a maximum within this
33603-4
Water-DME properties from molecular dynamics simulations
0 0.2 0.4 0.6 0.8 1
X
dme
-2.5
-2
-1.5
-1
-0.5
0
∆
V
m
ix
(c
m
3
/m
o
l)
SPC-E
TIP4P-Ew
Ref. [47]
a
0 0.2 0.4 0.6 0.8 1
X
dme
-3
-2.5
-2
-1.5
-1
-0.5
0
∆
H
m
ix
(
k
J/
m
o
l)
SPC-E - DME
TIP4P-Ew - DME
b
Figure 2. (Color online) Excessmixingmolar volume and excessmixing enthalpy of water-DMEmixtures
on composition.
0 0.2 0.4 0.6 0.8 1
X
dme
100
120
140
160
180
200
C
P
(
J/
m
o
l
K
)
SPC-E - DME
TIP4P-Ew - DME
a
0 0.2 0.4 0.6 0.8 1
X
dme
0
5
10
15
∆
C
P
m
ix
(J
(m
o
l
K
)
SPC-E - DME
TIP4P-Ew - DME
b
0 0.2 0.4 0.6 0.8 1
X
dme
0
50
100
150
200
∆
C
P
m
ix
/[
X
d
m
e
(1
-X
d
m
e
)]
SPC-E - DME
Ref. [48]
c
Figure 3. (Color online) Panel (a): Molar heat capacity on mixture composition. Panels (b) and (c):
Excess mixing heat capacity of water-DME mixtures on composition.
33603-5
J. Gujt, H. Dominguez, S. Sokolowski, O. Pizio
composition interval. Moreover, this peculiarity in ∆Cmix
P (Xdme) coincides along Xdme axis with the
extrema for the excess mixing volume and enthalpy in figure 2. The accuracy of simulation predictions
can be deduced from comparison with the experimental data selected from a big set of data given in
[49]. It appears that the simulation predictions agree with experiments reasonably well. We would like
to conclude the discussion of thermodynamic features of mixing just mentioning that a more elaborate
exploration of other fluctuation based thermodynamic properties, related to the experimental observations
provided in [50], will be given in a separate work.
3.2. Pair distribution functions, coordination numbers and hydrogen bonding
The microscopic structure of mixtures is usually and conveniently described in terms of various
pair distribution functions. However, only very limited insights in this aspect were given in previous
works. Specifically, only the pair distribution function, gi j(r), describing the evolution of configurations
of OW-Odme atoms upon changing the chemical composition in terms of Xdme was given in figure 6 of
[35] at T = 298 K, the evolution of OW-OW function was shown in figure 2S of [37] at T = 318 K.
Various combinations of models for water and DME have been involved. Unfortunately, the structure
factors from either X-ray or neutron diffraction experiments are not available in the literature, to our best
knowledge. Hence, the critical evaluation of the quality of simulation predictions similar to, e.g., [5]
cannot be performed for the moment. Therefore, we restrict ourselves to a brief discussion of the trends
of the behaviour of the microscopic structure in this work.
Our first important observation is that the intermolecular pair distribution function, Odme-Odme, is
rather inert or, in other words, exhibits very small changes in a wide interval of composition, panel (a)
of figure 4. The second observation concerns the OW-Odme distribution function, panel (b) of figure 4.
Computer simulations predict that this distribution function is sensitive to the value of Xdme but only at
small interparticle separations, i.e., close to their mutual contact. At larger distances, we do not observe
substantial changes of the shape of this distribution function. Thus, the structuring of water around ether
oxygens increases locally with increasing Xdme, miscibility of water and DME is actually expected. The
most drastic changes can be seen for the OW-OW distribution, panel (c) of figure 4. The first maximum
of water distribution strongly increases with increasing Xdme, i.e., when water fraction decreases. The
second and third maxima of water distribution grow as well. However, the asymptotic value at unity is
clearly seen. In other words, the water density becomes locally heterogeneous. However, the shape of
OW-OW distribution does not suggest the formation of large water clusters. These trends are qualitatively
similar to what was observed for another DME model combined with the SPC water model in [37]. The
observed behaviour combined with the trends of OW-Odme changes, can indicate a certain tendency to
the development of local heterogeneity and even to demixing at a local scale for a particular combination
of the models of each species, as already discussed in [35]. This is an important observation, because it
can have implications in the future studies of solutions of salts and/or complex organic molecules in such
combined solvents. In order to provide a better insight into the distribution of particles of each species,
we present visualization in two panels of figure 5. From the left-hand panel of this figure we learn that
the DME molecules are rather uniformly distributed in the medium with a predominant number of water
molecules, cf., the pair distribution function at Xdme = 0.1 in figure 4 (c). The Odme-Odme distribution is
of the type shown in figure 4 (a). The right-hand panel of figure 5 describes the situation at Xdme = 0.8,
cf. OW-OW distribution with very high first maximum and two well pronounced maxima at r ≈ 0.5 nm
and at ≈ 0.7 nm. The system is undoubtedly macroscopically homogeneous. However, the inspection of
water molecules distribution leads to a conclusion that local heterogeneities are present, the presence
of associates of a few water molecules is quite probable. It is worth noting at this point that a detailed
discussion of microheterogeneities in aqueous amide mixtures was given in [30]. We are unaware of
similar developments for water-DME mixtures.
The pair distribution functions yield the running coordination numbers by the relation,
ni(R) = 4πρj
R∫
0
gi j(r)r2dr, (1)
33603-6
Water-DME properties from molecular dynamics simulations
0.2 0.4 0.6 0.8 1 1.2
r (nm)
0
0.5
1
1.5
g
O
d
m
e -
O
d
m
e
(r
)
X
dme
= 0.933
X
dme
= 0.5
X
dme
= 0.333
SPC-E - DME
a
0.2 0.4 0.6 0.8 1 1.2
r (nm)
0
1
2
3
g
O
d
m
e -
O
W
(r
)
X
dme
= 0.933
X
dme
= 0.5
X
dme
= 0.1
SPC-E - DME
b
0.2 0.4 0.6 0.8 1 1.2 1.4
r (nm)
0
10
20
30
g
O
W
-O
W
(r
)
X
dme
= 0.8
X
dme
= 0.5
X
dme
= 0.1
SPC-E - DME
c
Figure 4. (Color online) Evolution of the pair distribution functions, Odme-Odme, Odme-OW and OW-OW
with changing solvent composition.
where ρj is the number density of species j. The first coordination number is obtained by putting
R = rmin, i.e., at the first minimum of the corresponding pair distribution function. The evolution of
the first coordination numbers of species with Xdme is given in figure 6 (a). It can be seen that the
cross coordination number grows smoothly, but remains rather small in the entire composition interval.
The Odme-Odme coordination number grows with an increasing fraction of organic species, but does
not substantially change in the interval from 0.3 up to DME-rich composition in accordance to what
was discussed for the behaviour of the corresponding pair distribution function. Thus, the structure of
organic subsystem remains relatively inert to changes of composition. The OW-OW coordination number
decreases in magnitude non-monotonously as a result of a decreasing fraction of water while Xdme
increases, and due to an increasing height of the first maximum of the OW-OW pair distribution function.
A less decline is observed in the interval of composition where the first maximum of the pair distribution
function increases most drastically.
Next,wewould like to comment on the hydrogen bonds network behaviour for themixtures in question.
The GROMACS software was straightforwardly applied to do that using default distance-angle criterion.
The average number of hydrogen bonds per water molecule, 〈nHB〉, as a function of composition, Xdme,
shown in figure 6 (b), exhibits certain similarities to the behaviour of coordination numbers discussed
above. At very low values of Xdme, the value for water-water 〈nHB〉 is high serving as an evidence of
the hydrogen bonded network between water molecules. If DME molecules are introduced into water,
the number of their mutual contacts increases, as it follows from the behaviour of the pair distribution
33603-7
J. Gujt, H. Dominguez, S. Sokolowski, O. Pizio
Figure 5. (Color online) Visualization of the distribution of water and DME species in the simulation
box for two values of mixture composition. Left panel is for Xdme = 0.1 whereas the right panel is at
Xdme = 0.8. Only the carbon sites are shown for DME (cyan), water oxygens and hydrogens are given by
red and green spheres, respectively.
0 0.2 0.4 0.6 0.8 1
X
dme
0
2
4
6
n
ij
(t
h
e
fi
rs
t
co
o
rd
in
at
io
n
n
u
m
b
er
s)
OW -OW
OW - O
dme
O
dme
- O
dme
SPC-E model
a
0 0.2 0.4 0.6 0.8 1
X
dme
0
1
2
3
4
<
n
h
b
>
water - DME
water - water
SPC-E water model
b
Figure 6. (Color online) Panel (a): Changes of the first coordination numbers nOdme-OW and nOW-OW
with mixture composition. Panel (b): Changes of the average number of hydrogen bonds between water
and DME molecules.
function OW-Odme. Consequently, the average number of H-bonds between waters decreases whereas
the fraction of bonds between water molecules and DME oxygens steadily increases. This behaviour is
qualitatively similar to some other water-organic solvent mixtures, see, e.g., figure 8 of our recent study
of water-DMSO mixtures [26]. In both cases, i.e., the DMSO and DME, no hydrogen bonding is feasible
in pure organic component. Most important is that neither the behavior of the coordination numbers as
function of intermolecular distance nor the average number of hydrogen bonds provide confirmation that
clusters of H-bonded water molecules can form in DME-water mixtures at high values of Xdme. Thus,
possible local heterogeneity of the distribution of water molecules deduced from the behaviour of the pair
distribution functions does not lead to the formation of big clusters or isolated “islands” of water species
distributed in the media of DME molecules at intermediate and high values of Xdme. In other words,
miscibility of species is preserved in the entire range of composition. Still, the formation of strongly
“associated” species involving groups of water and DME molecules cannot be discarded.
33603-8
Water-DME properties from molecular dynamics simulations
0 0.2 0.4 0.6 0.8 1
X
dme
0
0.05
0.1
0.15
0.2
X
i
SPC-E - DME
TGG
TTT
TGA
a
0 0.2 0.4 0.6 0.8 1
X
dme
0.625
0.75
X
T
G
T
SPC-E - DME
TGT
b
Figure 7. (Color online) Changes of the fractions of most populated conformations of DME molecules
with mixture composition.
Our final remark in this subsection about the microscopic structure of water-DME mixtures concerns
the conformations of DME molecules in mixtures as functions of the amount of the organic co-solvent,
Xdme (figure 7). Those were discussed in several recent publications [35–37]. We use the same definition
of conformers and the same nomenclature T , G, just G′ is denominated as A. Moreover, average values
for conformations population of molecules in liquid DME and water-DME mixtures are available from
Raman spectroscopy [51]. It is known that the modified TraPPE model in combination with TIP4P-Ew
water model leads to non-perfect, but in general reasonable description of the conformations population
upon DME fraction, see, e.g., figure 4 of [35]. We were able to reproduce fractions of all conformers
reported in [35], but failed to reproduce fractions of conformers reported in [37]. Accurate description
of the population of conformers is of importance on its own and, moreover, has implications for possible
future studies of the effects of solutes in water-DME solvents. Our results at T = 298.15 K, reported
in figure 7 exhibit similar trends as the behaviour reported by Fischer et al. at T = 318 K using the
TIP4P-Ew water model [35]. Of particular importance is that both the SPC-E and TIP4P-Ew combined
with the modified TraPPE successfully reproduce experimental observations that should decide which of
the conformers are most populated and how these populations change with Xdme.
3.3. Self-diffusion coefficients and the dielectric constant
The self-diffusion coefficients of water and DME species in our work were calculated from the
mean-square displacement (MSD) of a particle via Einstein relation,
Di =
1
6
lim
t→∞
d
dt
〈|ri(τ + t) − ri(τ)|2〉, (2)
where i refers to water or DME and τ is the time origin. Default settings of GROMACS were used for the
separation of the time origins. A set of trajectories coming from several consecutive simulations of 10 ns
was combined to get the entire trajectory not less than 60–70 ns. The fitting interval then was chosen from
≈ 10% to ≈ 50% of the entire trajectory to obtain Ddme and Dw. Moreover, to keep our consciousness
calm, we recalculated the self-diffusion coefficient for DME molecules using the center of mass to yield
Ddme. Two sets of results obtained were very close, possibly due to a rather small size of DME molecule.
A set of our results is given in figure 8. They concern the SPC-E water model in conjunction with the
modified TraPPE model for DME at T = 298.15 K. Previous comparisons, performed in [35] refer to the
TIP4P-Ewwater model with the modified TraPPEmodel atT = 318K. However, only the Dw values were
discussed. Experimental data at this temperature indicate a minimum of Dw at Xdme ≈ 0.2. Moreover,
according to Bedrov et al. [39] the experimental value for Ddme at Xdme = 1 is at 3.2. Our calculations
33603-9
J. Gujt, H. Dominguez, S. Sokolowski, O. Pizio
0 0.2 0.4 0.6 0.8 1
X
dme
0
1
2
3
4
D
i
(
1
0
-5
c
m
2
/s
)
SPC-E water
DME
Ref. [36]
Ref. [36]
i = w, dme
Figure 8. (Color online) Composition dependence of the self-diffusion coefficients of species in water-
DME mixture from NPT MD simulations.
yield a correct value for pure SPC-E water Dw = 2.54 and yield a minimum value of the self-diffusion
coefficient for water species at Xdme = 0.2333. On the other hand, we obtained Ddme ≈ 3.6 for pure DME.
In the absence of trustworthy experimental data at T = 298.15 K, we believe that the results both for
Dw and Ddme are at least qualitatively correct. In addition, we have plotted a rather limited set of points
obtained from simulations of the SPC-E water model and another DME model taken from the table IIISb
of [37]. It is difficult to explain a peculiar behaviour of Ddme at high values of Xdme (last two points). The
position of a minimum of Dw also seems to be unsatisfactory. From an overall shape of the behavior of
self-diffusion coefficients of species, one can conclude that the best mixing, according to, e.g., the excess
molar volume and enthalpy, corresponds to the minima of self-diffusion coefficients.
Our final remarks in this subsection concern the behaviour of the static dielectric constant, ε, of
mixtures in question. We explore it as function of the chemical composition. This property was not
explored in the previous works on the subject in spite of the experimental data available. Usually, the
static dielectric constant is calculated from the time-average of the fluctuations of the total dipole moment
of the system [52],
ε = 1 +
4π
3kBTV
(〈M2〉 − 〈M〉2), (3)
where kB is Boltzmann’s constant and V is the simulation cell volume.
The respective curves from simulations for combined water-DME mixtures (with the SPC-E and
TIP4P-Ew water models) are shown in figure 9 (a). General trends of the behaviour of this property
show that ε increases with decreasing Xdme starting from a low value of the pure substance without
intermolecular hydrogen bonding (DME) to amuch higher value corresponding to purewater.As it follows
from the comparison of the simulation results and experimental data [47], both models underestimate the
values for ε on the water-rich side and slightly overestimate the dielectric constant on the DME-rich side.
The static dielectric constant for pure DME due to our calculations is ε ≈ 8.9 whereas the experiment
yields 7.08 [47]. Nevertheless, the discrepancies between the simulation results and experiment are not
big in the entire interval of composition changes. As expected, the SPC-E model combined with the
modified TraPPE yields slightly better results in the water-rich interval of composition.
A more sensitive test is provided by a comparison of the excess dielectric constant [figure 9 (b)],
∆εmix = ε − (1 − Xdme)εwater − Xdmeεdme, with the experimental predictions [47]. Experimental points
indicate a negative deviation from perfection in the entire composition range. Interestingly, this behaviour
is contrary to what follows for water-DMSO liquid mixtures [26]. Maximal deviation from the ideal type
behaviour reported from the experimental measurements for the system in question is at Xdme = 0.3. The
simulation results reproduce the position of minimum successfully. However, the magnitude of deviation
33603-10
Water-DME properties from molecular dynamics simulations
0 0.2 0.4 0.6 0.8 1
X
dme
20
40
60
80
ε
Ref. [46]
SPC-E - DME
TIP4P-Ew - DME
a
0 0.2 0.4 0.6 0.8 1
X
dme
-30
-25
-20
-15
-10
-5
0
∆
ε
m
ix
Ref. [46]
TIP4P-Ew - DME
SPC-E - DME
b
Figure 9. (Color online) Panel (a): Composition dependence of the static dielectric constant of water-DME
mixtures. Panel (b): Excess mixing dielectric constant.
is underestimated from the simulated models. The SPC-E with a modified TraPPE model is closer to the
experimental values [47], compared with the TIP4P-Ew. Another set of experimental data concerning
∆εmix dependence on composition was reported in [53]. Again, the minimum value of the excess mixing
static dielectric constant was observed at Xdme ≈ 0.3. However, the value at minimum is around 25,
showing close agreement of the SPC-E-TraPPE model predictions with these experimental observations.
It is worth mentioning that a negative deviation of the excess dielectric constant for mixtures surely results
from the presence of “associated”mixed species of water andDMEmolecules with favourable correlation
of the dipole moments of molecules, i.e., their symmetrical orientation contributing to polarizability, and
certain amount of cross hydrogen bonds. Moreover, the lifetime of these species or complexes seems to
be such that it can be detected by the dielectric constant measurements.
4. Summary and conclusions
The mixtures explored in this work are one of the examples from the class of systems composed
of water and organic co-solvent. They are of much importance in laboratory studies with possible
applications in chemistry and bio-related areas.
We have performed an extensive set of molecular dynamic simulations in the isobaric-isothermal
ensemble to study the density, mixing properties and the microscopic structure of water-DME mixtures
in the entire range of a solvent composition. The self-diffusion coefficients of species and the dielectric
constant were calculated as well. All the simulations were performed at room temperature and ambient
pressure, 1 bar. Two water models (SPC-E and TIP4P-Ew), combined with the modified TraPPE model
for DME [35], were studied; we consider this as a first step of systematic studies of mixtures of water and
DME at different thermodynamic states using nonpolarizable models.
From a comparison with the available experimental data for different properties and with the results of
other authors on this and related systems, we can conclude that the predictions obtained are qualitatively
correct and give a physically sound picture of the properties explored. We observed that practically all
the properties investigated are sensitive to the composition of water-organic liquid solvent.
The principal conclusions of the present study can be summed up as follows. We explored the
evolution of the microscopic structure in terms of the pair distribution functions together with the first
coordination numbers of species. In this respect, the simulation results evidence that the structure of the
subsystem of DME species is much more inert or much less sensitive to the composition, in comparison
with the structure of an aqueous subsystem. The pair distribution functions for water species evidence that
a heterogeneous density distribution at local scale can develop upon adding the DME molecules. These
33603-11
J. Gujt, H. Dominguez, S. Sokolowski, O. Pizio
trends of changes of the microscopic structure bear a similarity to some other water-organic co-solvent
mixtures, see, e.g., [54, 55].
However, from the behaviour of the coordination numbers in the system explored, we have not found
that water clusters of significant size can be formed. The cross correlations seem to be not very strong
as it follows from the corresponding coordination number, but mixing is well pronounced. Thus, the
“associated” species involving water and DME molecules or their groups are formed in the system, with
or without hydrogen bonds. Statistical features of the hydrogen bonding in water and of water-organic
co-solvent bonds do not show a peculiar behaviour, in comparison to a qualitatively similar mixture of
water with DMSO [26]. On the other hand, the analyses of the most popular conformations and their
fractions as function of Xdme at room temperature are in accordance with the recently reported results
of [35].
Dynamic properties have been studied from the mean square displacements and are given in terms of
self-diffusion coefficients of species, Dw and Ddme. Both of them exhibit a minimum in the interval of
composition that corresponds to most “packed” structures according to the behaviour of mixing volume.
The values of self-diffusion coefficients of species for pure components are reasonably well described.
Concerning the dependence of the static dielectric constant on composition, we observe that its excess is
better described while using the SPC-E water model in comparison with the TIP4P-Ew model. It would
be of interest to relate the behaviour of the static dielectric constant on composition with refractive index
and viscosity data. However, this would require an additional computer simulation work.
At the present stage of the development, the missing elements worth a more detailed investigation
include the application of other, more elaborate, force fields for the DME molecules for the description
of water-DME mixtures. Wider insights into the behaviour of dynamic and dielectric properties by
exploration, e.g., the relaxation times, hydrogen-bonds lifetime and complex dielectric constant, would be
desirable. Unfortunately, the structure factors of the mixtures in question from the diffraction experiments
are unavailable. Hence, for the moment we are unable to perform a detailed study of the microscopic
structure along the lines proposed in [56] and recently applied for water-methanol mixtures [5].
Our interest into the properties of water-DME mixtures has been principally inspired by possible and
challenging extensions. One of them, rather straightforward, is the application of molecular dynamics
simulations to explore longer polyoxyethylene oligomers that exhibit more complex and richer properties.
Another challenging line of research is to explore the solutions with ionic solutes or complex molecules
in water-DMEmixtures in close similarity to the previous combined experimental and simulation studies,
in the spirit of [57–60] or of e.g. [61–65]. In this latter group of works, the phase diagrams of solute-
combinedwater-organic solvent systemswere described using only experimental tools. Thus, the proposed
description of possible phase separation mechanisms seems to be vague. Actually, the problem of ionic
solutes in water-organic solvent mixtures has been successfully considered only for the case of two solvent
components being immiscible, see, e.g., [66]. These problems are now under study in our laboratory.
Acknowledgements
O.P. is grateful to D. Vazquez and M. Aguilar for technical support of this work at the Institute of
Chemistry of the UNAM.
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Комп’ютерне моделювання методом молекулярної
динамiки в iзобарично-iзотермiчному ансамблi
властивостей модельних сумiшей вода-1,2-диметоксиетан
Ю. Гуйт1, Г. Домiнгез2, С. Соколовскi3, O. Пiзiо2
1 Кафедра теоретичної фiзики, хiмiчний факультет, унiверситет Дуйсбург-Ессен, D-45141 Ессен, Нiмеччина
2 Iнститут матерiалознавства, Нацiональний автономний унiверситет м.Мехiко,Мехiко,Мексика
3 Вiддiл моделювання фiзико-хiмiчних процесiв, унiверситет Марiї-Склодовської Кюрi, Люблiн, Польща
Для того,щоб дослiдити широкий набiр властивостей модельних сумiшей вода-1,2-диметоксиетан (DME)
в залежностi вiд концентрацiї, проведено комп’ютерне моделювання методом молекулярної динамiки в
iзобарично-iзотермiчному ансамблi. Для води застосовано моделi SPC-E i TIP4P-Ew, а для DME — моди-
фiковану модель TraPPE. Нашим основним завданням було дослiдити тенденцiю поведiнки структурних
властивостей в термiнах радiальних функцiй розподiлу, координацiйних чисел та чисел водневих зв’язкiв
мiж молекулами рiзних сортiв, а також конформацiї молекул DME. Вивчено термодинамiчнi властивостi,
такi як густина, молярний об’єм, ентальпiя змiшування i питома теплоємнiсть при постiйному тиску. Накi-
нець, обчислено i проаналiзовано коефiцiєнти самодифузiї сортiв i дiелектричну сталу системи.
Ключовi слова: сумiшi вода-DME, термодинамiчнi властивостi, коефiцiєнти самодифузiї, дiелектрична
стала, молекулярна динамiка
33603-14
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https://doi.org/10.1021/jp305516g
https://doi.org/10.1021/jp412162c
Introduction
Model and simulation details
Results and discussion
Density and mixing properties
Pair distribution functions, coordination numbers and hydrogen bonding
Self-diffusion coefficients and the dielectric constant
Summary and conclusions
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