Phase equilibria and interfacial properties of two-dimensional Yukawa fluids
Molecular dynamics simulations of two-dimensional soft Yukawa fluids are performed to analyze the effect that the range of interaction has on coexisting densities and line tension. The attractive one-component fluid and equimolar mixtures containing positive and negative particles are studied at dif...
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| Cite this: | Phase equilibria and interfacial properties of two-dimensional Yukawa fluids / G.A. Méndez-Maldonado, M. González-Melchor, J. Alejandre // Condensed Matter Physics. — 2012. — Т. 15, № 2. — С. 23002:1-8 . — Бібліогр.: 35 назв. — англ. |
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| author | Méndez-Maldonado, G.A. González-Melchor, M. Alejandre, J. |
| author_facet | Méndez-Maldonado, G.A. González-Melchor, M. Alejandre, J. |
| citation_txt | Phase equilibria and interfacial properties of two-dimensional Yukawa fluids / G.A. Méndez-Maldonado, M. González-Melchor, J. Alejandre // Condensed Matter Physics. — 2012. — Т. 15, № 2. — С. 23002:1-8 . — Бібліогр.: 35 назв. — англ. |
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| description | Molecular dynamics simulations of two-dimensional soft Yukawa fluids are performed to analyze the effect that the range of interaction has on coexisting densities and line tension. The attractive one-component fluid and equimolar mixtures containing positive and negative particles are studied at different temperatures to locate the region where the vapor-solid and vapor-liquid phases are stable. When the range of interaction decreases, the critical temperature of the attractive one-component systems decreases. However, for the charged mixtures it increases, and this opposite behaviour is understood in terms of the repulsive interactions which are dominant for these systems. The stable phase diagram of two-dimensional fluids is defined for smaller values of the decay parameter λ than that of fluids in three dimensions. The two-dimensional attractive one-component fluid has stable liquid-vapor phase diagram for values of λ, in contrast to the three-dimensional case, where stability has been observed even for values of λ<15. The same trend is observed in equimolar mixtures of particles carrying opposite charges.
Для того, щоб проаналiзувати, як впливає область взаємодiї на спiвiснуюючi густини i лiнiйний натяг, здiйснено симуляцiї методом молекулярної динамiки двовимiрних м’яких Юкава-плинiв. Притягальний однокомпонентний плин та еквiмолярнi сумiшi, що мiстять позитивнi i негативнi частинки, дослiджувалися при рiзних температурах таким чином, щоб визначити область, в якiй є стiйкими фази пара-тверде тiло i пара-рiдина. Зi зменшенням областi взаємодiї зменшується критична температура притягальних однокомпонентних систем. Проте для заряджених сумiшей вона зростає, i ця вiдмiннiсть у поведiнцi по-яснюється наявнiстю вiдштовхувальної взаємодiї, яка домiнує в цих системах. Дiаграма стiйкої фази двовимiрних плинiв є отримана для менших значень параметра затухання λ, нiж у випадку тривимiрних плинiв. Двовимiрний притягальний однокомпонентний плин має стiйку фазову дiаграму рiдина-пара для значень λ < 3, що вiдрiзняється вiд тривимiрного випадку, для якого стiйкiсть спостерiгається навiть для значень λ < 15. Така ж тенденцiя спостерiгається в еквiмолярних сумiшах протилежно заряджених частинок.
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Condensed Matter Physics, 2012, Vol. 15, No 2, 23002: 1–8
DOI: 10.5488/CMP.15.23002
http://www.icmp.lviv.ua/journal
Phase equilibria and interfacial properties of
two-dimensional Yukawa fluids
G.A. Méndez-Maldonado1, M. González-Melchor2, J. Alejandre3∗
1 Facultad de Ciencias Físico-Matemáticas, Benémerita Universidad Autónoma de Puebla,
Apartado Postal 1152, 72570, Puebla, México
2 Instituto de Física “Luis Rivera Terrazas”, Benemérita Universidad Autónoma de Puebla,
Apartado Postal J–48, 72570, Puebla, México
3 Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa,
Av. San Rafael Atlixco 186, Col. Vicentina, 09340, México Distrito Federal, México
Received February 23, 2012
Molecular dynamics simulations of two-dimensional soft Yukawa fluids are performed to analyze the effect that
the range of interaction has on coexisting densities and line tension. The attractive one-component fluid and
equimolar mixtures containing positive and negative particles are studied at different temperatures to locate the
region where the vapor-solid and vapor-liquid phases are stable. When the range of interaction decreases, the
critical temperature of the attractive one-component systems decreases. However, for the charged mixtures it
increases, and this opposite behaviour is understood in terms of the repulsive interactions which are dominant
for these systems. The stable phase diagram of two-dimensional fluids is defined for smaller values of the decay
parameter λ than that of fluids in three dimensions. The two-dimensional attractive one-component fluid has
stable liquid-vapor phase diagram for values of λ< 3, in contrast to the three-dimensional case, where stability
has been observed even for values of λ < 15. The same trend is observed in equimolar mixtures of particles
carrying opposite charges.
Key words: phase diagram, Yukawa fluids, interfacial properties
PACS: 05.70.Fh, 64.70.F-, 65.20.De, 68.03.Cd
1. Introduction
The location of stable phases in systems with molecular interactions has been a subject of great inter-
est in many applications such as simple liquids, electrolyte solutions, colloidal suspension and water. It is
well known that fluids with only repulsive interactions have a phase diagram that shows fluid-solid tran-
sition [1]. Attractive forces are needed to develop a vapor-liquid phase separation [2]. Several methods,
among them, molecular simulations, theory of liquids and experiments are used to obtain information
about the phase diagram of atomic and molecular fluids. Although it is possible nowadays to obtain the
phase boundaries using atomistic simulations of molecules including internal degrees of freedom [3, 4],
from theoretical and simulation points of view, it is more convenient to use simple potential models such
as square well (SW), Lennard-Jones (LJ), Yukawa and Coulomb interactions. The effect that parameters
of the potential has on the phase diagram in general, and in particular, on the critical properties can be
systematically analyzed by computer simulations. The SW, LJ and attractive hard-core Yukawa (AHCY)
potentials have a short-ranged repulsion and the attraction is long or variable-ranged. For these models
it has been established in three-dimensional (3D) systems that the critical temperature decreases as the
attraction decreases [5–9]. For very small ranges of attraction, when the vapor-liquid or liquid-solid phase
diagrams for the AHCY model become metastable, it has been found that the critical point is below the
triple point [8].
∗E-mail: jra@xanum.uam.mx
© G.A. Méndez-Maldonado, M. González-Melchor, J. Alejandre, 2012 23002-1
http://dx.doi.org/10.5488/CMP.15.23002
http://www.icmp.lviv.ua/journal
G.A. Méndez-Maldonado, M. González-Melchor, J. Alejandre
The phase diagram and interfacial properties of ionic fluids, where the interaction has attraction and
repulsion, has also been studied in 3D for the restricted primitive model (an electroneutral equimolar
mixture of particles having the same size and carrying opposite charges) [10, 11] and for ionic fluids with
asymmetry in size and charge [12–14]. The effect of range of interaction on the phase diagram of ionic
fluids has been analyzed using the Yukawa potential. Mier-y-Terán et al. [15] used the mean spherical
approximation theory to calculate the critical properties of mixtures containing positive and negative
particles at different range of interaction. They predicted that as the range of interaction decreases the
critical temperature increases, it reaches amaximum and then decreases. That finding is counterintuitive
in the sense that less attractive potentials increase the critical temperature. The surface tension for mix-
tures of charged particles using the Yukawa model have also been reported using molecular dynamics
[16]. Fortini et al. [17] performed computer simulations to locate the regions where the vapor-liquid and
liquid-solid were stable. Their conclusions were that stable liquid-vapor phase diagrams were found for
values of the screening parameter λ < 4, in disagreement with the results of Caballero et al. [18] where
the phase diagram was stable for λ < 10. The results of Caballero et al. were obtained for a slightly dif-
ferent potential, but according to Fortini et al., the difference in the results were not related with the
potential. Hynninen and Panagiotopoulos [19] found that vapor-liquid phase transition of highly charged
colloids is metastable with respect to the vapor-solid phase diagram because at high temperatures the
interaction becomes purely repulsive.
Apart from the work in 3D, it is also interesting to understand the phase behavior of ionic particles
in two-dimensions. Experimental results on quasi two-dimensional (2D) colloidal suspensions show in-
teresting properties [20, 21]. The phase diagrams of 2D systems obtained by computer simulations are
scarce. The vapor-liquid and fluid-solid phase diagrams of the LJ fluid in two dimensions were obtained
by Barker et al. [22] in 1981 using a liquid-state perturbation theory and Monte Carlo simulations. They
found that the phase diagramwas qualitatively similar to the 3D system. Santra et al. [23] in 2008 studied
the nucleation rate of a liquid phase. They used the LJ model and Monte Carlo simulations to validate the
predictions of the classical nucleation theory. They calculated for the first time the line tension of the 2D
LJ fluid. Later on, Santra and Bagchi [24] obtained the vapor-liquid phase diagram and line tension of the
LJ model at different temperatures. The critical temperature from simulations for the 3D LJ is around 2.5
times greater than its value in 2D. The restricted primitive model of ions in two dimensions was studied
byWeis et al. [25] usingMonte Carlo simulations and integral equations theory. For this system the critical
temperature in the 3Dmodel is around 1.3 times its value in 2D. Analyzing the stability of phase diagrams
in 2Dmight be useful to understand the phase separation in 3D and to investigate new phenomena which
are not found in 3D.
The main goal of this work is to analyze the effect that the range of interaction has on coexisting den-
sities and line tension of 2D fluids that interact with the soft Yukawamodel. To our best knowledge, there
have neither been reported any phase diagrams nor surface tension for these fluids. The one-component
systems with attractive interactions and the two-component mixture of positive and negative particles
are studied at different ranges of interaction.
This work is organized as follows: The potential model and definition of the calculated properties are
presented in section 2. Results are discussed in section 3 and finally Concluding remarks and References
are given.
2. Potential model and calculated properties
The soft Yukawa potential is used to simulate the two-dimensional fluids of pure attractive spheres
and equimolar mixtures of particles carrying the opposite charge,
U (r )=
[
(σ
r
)225
+
qαqβe−λ(r /σ−1)
r /σ
]
fmin (2.1)
where λ−1 is a measure of the range of interaction in dimensionless units and qα is the charge of particle
α in themixture case. The particles are all the same sizeσ. For the attractive one-component fluid qαqβ =
−1. The factor fmin = 1.075 is included to have a potential which is zero at r = σ and close to −1 at the
23002-2
Two-dimensional Yukawa fluids
minimum for the attractive pairs. The short-ranged soft model, instead of the hard sphere model, has
been used earlier to study interfacial properties of the restricted primitive model [11, 26] and ions with
asymmetry in size and charge [27]. The results for the soft model were found to be in good agreement
with those where the short range repulsion is given by the hard sphere potential. The advantage of the
soft model is that it is straightforward to use molecular dynamics of continuous models.
Reduced units are used in this work for the two-dimensional systems: distance r ∗ = r /σ, energy u∗ =
u/ǫ (where ǫ = U (rmin)), temperature T ∗ = kT /ǫ, density ρ∗ = ρσ2, time ∆t∗ = ∆t(ǫ/mσ2)1/2, pressure
p∗ = pσ2/ǫ and line tension γ∗ = γσ/ǫ. The density profile, ρ(x), was obtained as,
ρ(x) =
〈N (x, x +∆x)〉
∆A
(2.2)
where 〈N (x, x +∆x)〉 is the average number of particles with position between x and x +∆x and ∆A is
the area of a slab.
The line tension of a planar interface, using the mechanical definition of the atomic pressure, [29] is
γ= 0.5Lx
[
〈Pxx 〉−〈Py y〉
]
, (2.3)
where Lx is the length of the simulation cell in the longest direction and Pαα (α = x, y) are diagonal
components of the pressure tensor. The factor 0.5 outside the squared brackets takes into account the
two symmetrical interfaces in the simulation.
The component Pxx of the pressure tensor was calculated as,
Pxx A =
∑
i
mi v2
xi +
∑
i
∑
j>i
Fi j ·ri j , (2.4)
where vxi and mi are the velocity in the x direction and the mass of particle i , respectively, A is the area
of the system and ri j = ri − r j with ri being the position of particle i . A similar expression for Py y was
used. The force between particles i and particle j is,
Fi j =−
∂u(ri j )
∂ri j
ri j
ri j
. (2.5)
3. Results
Extensive molecular dynamics simulations, with a parallel program, were performed on particles
interacting with the soft Yukawa potential at different ranges of interaction λ−1. All the simulations to
study inhomogeneous systems were carried out in non-squared simulation cells, keeping the total density
and temperature (NAT) constant.
3.1. One-component systems
Results for the one-component systems where particles interact with the attractive soft Yukawa po-
tential were obtained for values of the reciprocal range of interaction λ= 1, 1.8, 3, 4 and 6. The value of
λ= 1.8 was chosen to make a direct comparison with the 2D LJ fluid. It was shown in the previous work
[30] that in 3D the hard core Yukawa model with λ= 1.8 gave equivalent results with the LJ potential.
Initially a number of 400 particleswere placed in themiddle of the simulation cell at a reduced density
of 0.4 and the velocities randomly distributed. The dimensions of the simulation cell were Lx = 60σ and
Ly = 15σ. The equations of motion were solved using the velocity Verlet algorithm with a reduced time
step of ∆t∗ = 0.0005. The temperature was kept constant with a global thermostat using a Nosé-Hoover
chains of 4 thermostats [28] with parameter of 0.01.The cut-off distance was 6σ for all the simulations of
pure fluids. The systems evolved to reach the equilibrium state where a liquid slab was surrounded by
vapor [26]. The systems in all cases were followed by 80 blocks of 106 time steps.
The density profiles for λ= 1.8 are shown in figure 1. Two symmetrical interfaces are observed with
a large amount of particles in the liquid and vapor regions which allows one to obtain the corresponding
coexisting densities. Similar density profiles are found for λ= 1.0, 3.0 and 6.0 not shown.
23002-3
G.A. Méndez-Maldonado, M. González-Melchor, J. Alejandre
Figure 1. (Color online) Density profiles for attrac-
tive soft Yukawa one-component systems with λ=
1.8 at different reduced temperatures.
Figure 2. (Color online) Density profiles for attrac-
tive soft Yukawa one-component systems with λ=
4 at different reduced temperatures.
The density profiles for λ = 4 are shown in figure 2. There was not observed a vapor-liquid phase
separation but vapor-solid equilibrium in a very narrow range of temperatures, from 0.30 to 0.315. Large
densityfluctuations were found at a reduced temperature of 0.32 but awell defined vapor-liquid interface
was not stabilized. Homogeneous fluids were found for reduced temperatures above 0.35. The longest
size of the simulation cell was increased in order to check if the phase separation from vapor-solid to
vapor-liquid was not related to finite size effects. The two-dimensional attractive soft Yukawa model
seems to have a stable vapor-liquid equilibrium for values of λ around 3, this is contrary to the 3D case
where the same phase equilibrium is stable for values of λ less than 15 [31].
Figure 3. (Color online) Liquid-vapor phase dia-
gram for attractive one-component systems with
the inverse of the interaction range λ = 1.0, 1.8,
3.0, 4.0 and 6.0.
Figure 4. (Color online) Line tension for attractive
one- component systems with λ = 1.0 and 1.8 are
shown with filled circles. The results for the 2D
Lennard-Jones model [24] are shown with open
circles.
The phase diagram of the attractive soft Yukawa potential is shown in figure 3 for different values of
λ. As expected, the critical temperature decreases as the range of interaction decreases. At low tempera-
tures the vapor-solid equilibrium is observed for values of λ= 1.8 and 4. The vapor-liquid transition was
not found for λ= 4, it is metastable with respect to the vapor-solid equilibrium. The critical density and
temperature for λ= 1 and λ= 1.8 were estimated by fitting the coexisting densities to a rectilinear diam-
eter law with a critical exponent of 1/8 according to a two-dimensional Ising model system [32, 33] and
23002-4
Two-dimensional Yukawa fluids
experimental results for methane [34]. The final results were (0.36,0.72) and (0.38,0.50), respectively. The
critical temperature using the coexisting densities for λ= 1.0 might be around T ∗ = 0.8 but the estimated
value using the critical exponent of 1/8 is much smaller. The 2D soft Yukawa with λ= 1.8 and LJ models
give nearly the same results as shown in figure 3.
The line tension of the attractive soft Yukawamodel is shown in figure 4 as a function of temperature,
its decay almost following a linear function. The critical temperature can be obtained when line tension
is zero, the estimated values for λ = 1.0 and λ = 1.8 are 0.53 and 0.83, respectively. The result for λ = 1
is quite different from the value obtained using the coexisting densities and critical exponent of 1/8.
The results for the two-dimensional LJ model, also shown in the figure, are in good agreement with the
attractive soft Yukawa model with λ= 1.8.
The phase diagram and line tension of 2D and 3D attractive soft Yukawa fluids are completely dif-
ferent. The vapor-liquid phase diagram in 3D is stable for values of λ < 15, i.e., for very short ranges
of interaction, whereas in the 2D case the stability is found for λ < 3. Clearly, the strength of the global
attraction needed in 2D to produce the separation is quite different from that in 3D.
3.2. Mixture of particles carrying opposite charges
Molecular dynamics simulations on equimolar binary mixtures of equal-size particles carrying op-
posite charges are carried out to analyze the effect that the range of interaction has on phase stability
and line tension. The systems contained 1000 particles in a non-squared simulation cell of Lx = 150σ
and Ly = 38σ dimensions. The potential was truncated at 15σ and the reduced time step was 0.0005. The
simulation protocol to obtain the coexisting densities and line tension was the same as that used for the
attractive soft Yukawa model described above. The systems were followed for at least 100 blocks of 106
time steps. The average properties were obtained from the last 40 blocks.
Figure 5. (Color online) Density profiles for the soft Yukawa mixture of charged particles with λ = 2.0.
The temperatures are given in the figure.
The phase diagram for the same system but in 3D has been calculated [17] and it was found that the
vapor-liquid equilibriumwas stable for values of λ< 4. In order to find the region where the vapor-liquid
transition occurred, several simulations were performed in this work using λ= 2. The difference in criti-
cal temperature for the restricted primitive model in 2D and 3Dwas less than 25 % (see the Introduction).
We expected to find the same trend in the binarymixtures using the soft Yukawamodel. However, we did
not find any evidence of vapor-liquid phase separation using the direct simulation of interfaces. A vapor-
solid equilibriumwas observed for reduced temperatures as low as 0.106. The amount of vapor increases
when the reduced temperature rises to 0.112 but the solid phase still remains stable. At T ∗ = 0.116 the
particles behave as a homogenous fluid, see figure 5. As in the 3D mixture of charged particles with oppo-
site sign interacting with the hard core Yukawa model, the critical temperature increases as the range of
interaction decreases [15, 17], i.e., the system increases its liquid density as λ increases. In fact, for values
23002-5
G.A. Méndez-Maldonado, M. González-Melchor, J. Alejandre
of λ> 4, the vapor-liquid phase diagram is meta-stable with respect to the vapor-solid equilibrium. In the
same way, the possibility of finding a vapor-liquid phase transition in 2D charged mixtures would be in
the direction of increasing the range of interaction.
Therefore, MD simulations were performed using λ = 1.0. In this case, a vapor-liquid phase separa-
tion was found in a very narrow range of reduced temperatures, from 0.078 to 0.08. The liquid contains
alternated particles with opposite charges and large voids are observed, see figure 6 for T ∗ = 0.79. In the
vapor phase, the particles contain a large cluster and some particles form linear chains and rings.
Figure 6. (Color online) Snapshot for the soft Yukawa mixture of charged particles with λ= 1.0 and T∗ =
0.079.
The density profiles are shown in figure 7 and have large fluctuations. However, the liquid and vapor
can be estimated when simulations are run for several millions of configurations. The analysis of the
radial distribution function for the region with higher density shows a behavior of a liquid.
Figure 7. (Color online) Density profiles at different temperatures for the soft Yukawamixture of charged
particles with λ= 1.0.
The line tension for binary mixtures was also calculated and the results are shown in figure 8. As
found in simple fluids, the line tension decays with temperature.
4. Concluding remarks
Themain conclusion found in this work is that the stability of vapor-liquid phase diagram in 2D fluids
requires longer ranges of interactions than in 3D systems in both the one-component soft Yukawa model
and the binary mixture of soft spheres carrying charges with the opposite sign. The range of interaction
for these models increases when the inverse screening parameter λ decreases. The metastable vapor-
liquid transition, with respect to the vapor-solid equilibrium, for the one component model in 2D is found
for values of λ> 4 while in the 3D case it is found for λ> 15, i.e., for very short ranges of interaction. For
the binary mixture in 2D, metastability occurs for λ > 1 in contrast to λ > 4 observed in the 3D case. A
possible explanation might be given using the classical nucleation theory [35] arguments. The formation
of a liquid phase in that theory requires that particles in ametastable vapor phase should nucleate up to a
critical size. The number of particles in a nucleus of 2D fluids for the same range of interaction is smaller
23002-6
Two-dimensional Yukawa fluids
Figure 8. Line tension as a function of temperature for soft Yukawa mixture of charged particles with
λ= 1.0.
than in 3D because in 3D the particles are in a sphere while in 2D they are in a circle. The particles in 2D
have to interact longer distances than in 3D for the nucleus to reach the critical size.
On the other hand, the vapor-liquid phase diagram and line tension for the one-component attractive
soft Yukawa model are in good agreement with those obtained using the LJ in 2D.
Acknowledgements
G.A.M.M. and M.G.M. acknowledge financial support from CONACyT (Project 129034), VIEP–BUAP
(GOMM–EXC10–I), PROMEP/103.5/07/2594 and CA Física Computacional de la Materia Condensada. J.A.
thanks Conacyt (Project 81667) for financial support and to Laboratorio de Supercómputo for time allo-
cation.
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Фазова рiвновага i мiжфазнi властивостi двовимiрних
Юкава-плинiв
Ґ.А. Мендес-Мальдонадо1, М. Ґонсалес-Мельчор2, Х. Алехандре3
1 Факультет фiзико-математичних наук, Автономний унiверситет Пуебла, 72570, Пуебла, Мексика
2 Iнститут фiзики, Автономний унiверситет Пуебла, 72570, Пуебла, Мексика
3 Хiмiчний факультет, Автономний унiверситет Метрополiтана-Iстапалапа, 09340, Федеральний округ
Мехiко, Мексика
Для того, щоб проаналiзувати, як впливає область взаємодiї на спiвiснуюючi густини i лiнiйний натяг,
здiйснено симуляцiї методом молекулярної динамiки двовимiрних м’яких Юкава-плинiв. Притягальний
однокомпонентний плин та еквiмолярнi сумiшi, що мiстять позитивнi i негативнi частинки, дослiджува-
лися при рiзних температурах таким чином, щоб визначити область, в якiй є стiйкими фази пара-тверде
тiло i пара-рiдина. Зi зменшенням областi взаємодiї зменшується критична температура притягальних
однокомпонентних систем. Проте для заряджених сумiшей вона зростає, i ця вiдмiннiсть у поведiнцi по-
яснюється наявнiстю вiдштовхувальної взаємодiї, яка домiнує в цих системах. Дiаграма стiйкої фази дво-
вимiрних плинiв є отримана для менших значень параметра затухання λ, нiж у випадку тривимiрних
плинiв. Двовимiрний притягальний однокомпонентний плин має стiйку фазову дiаграму рiдина-пара для
значень λ< 3, що вiдрiзняється вiд тривимiрного випадку, для якого стiйкiсть спостерiгається навiть для
значень λ < 15. Така ж тенденцiя спостерiгається в еквiмолярних сумiшах протилежно заряджених ча-
стинок.
Ключовi слова: фазова дiаграма, Юкава-плини, мiжфазнi властивостi
23002-8
http://dx.doi.org/10.1103/PhysRevLett.98.198301
http://dx.doi.org/10.1103/PhysRevLett.77.1897
http://dx.doi.org/10.1103/PhysRevLett.80.5802
http://dx.doi.org/10.1016/0378-4371(81)90222-3
http://dx.doi.org/10.1063/1.3037227
http://dx.doi.org/10.1063/1.3206735
http://dx.doi.org/10.1063/1.477371
http://dx.doi.org/10.1063/1.1861878
http://dx.doi.org/10.1080/00268970902780270
http://dx.doi.org/10.1080/00268970210121669
http://dx.doi.org/10.1063/1.1384553
http://dx.doi.org/10.1063/1.3357352
http://dx.doi.org/10.1103/PhysRev.65.117
http://dx.doi.org/10.1103/PhysRev.85.808
http://dx.doi.org/10.1103/PhysRevLett.53.170
Introduction
Potential model and calculated properties
Results
One-component systems
Mixture of particles carrying opposite charges
Concluding remarks
|
| id | nasplib_isofts_kiev_ua-123456789-120270 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-07T15:42:38Z |
| publishDate | 2012 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Méndez-Maldonado, G.A. González-Melchor, M. Alejandre, J. 2017-06-11T14:24:11Z 2017-06-11T14:24:11Z 2012 Phase equilibria and interfacial properties of two-dimensional Yukawa fluids / G.A. Méndez-Maldonado, M. González-Melchor, J. Alejandre // Condensed Matter Physics. — 2012. — Т. 15, № 2. — С. 23002:1-8 . — Бібліогр.: 35 назв. — англ. 1607-324X PACS: 05.70.Fh, 64.70.F-, 65.20.De, 68.03.Cd DOI:10.5488/CMP.15.23002 arXiv:1207.3258 https://nasplib.isofts.kiev.ua/handle/123456789/120270 Molecular dynamics simulations of two-dimensional soft Yukawa fluids are performed to analyze the effect that the range of interaction has on coexisting densities and line tension. The attractive one-component fluid and equimolar mixtures containing positive and negative particles are studied at different temperatures to locate the region where the vapor-solid and vapor-liquid phases are stable. When the range of interaction decreases, the critical temperature of the attractive one-component systems decreases. However, for the charged mixtures it increases, and this opposite behaviour is understood in terms of the repulsive interactions which are dominant for these systems. The stable phase diagram of two-dimensional fluids is defined for smaller values of the decay parameter λ than that of fluids in three dimensions. The two-dimensional attractive one-component fluid has stable liquid-vapor phase diagram for values of λ, in contrast to the three-dimensional case, where stability has been observed even for values of λ<15. The same trend is observed in equimolar mixtures of particles carrying opposite charges. Для того, щоб проаналiзувати, як впливає область взаємодiї на спiвiснуюючi густини i лiнiйний натяг, здiйснено симуляцiї методом молекулярної динамiки двовимiрних м’яких Юкава-плинiв. Притягальний однокомпонентний плин та еквiмолярнi сумiшi, що мiстять позитивнi i негативнi частинки, дослiджувалися при рiзних температурах таким чином, щоб визначити область, в якiй є стiйкими фази пара-тверде тiло i пара-рiдина. Зi зменшенням областi взаємодiї зменшується критична температура притягальних однокомпонентних систем. Проте для заряджених сумiшей вона зростає, i ця вiдмiннiсть у поведiнцi по-яснюється наявнiстю вiдштовхувальної взаємодiї, яка домiнує в цих системах. Дiаграма стiйкої фази двовимiрних плинiв є отримана для менших значень параметра затухання λ, нiж у випадку тривимiрних плинiв. Двовимiрний притягальний однокомпонентний плин має стiйку фазову дiаграму рiдина-пара для значень λ < 3, що вiдрiзняється вiд тривимiрного випадку, для якого стiйкiсть спостерiгається навiть для значень λ < 15. Така ж тенденцiя спостерiгається в еквiмолярних сумiшах протилежно заряджених частинок. G.A.M.M. and M.G.M. acknowledge financial support from CONACyT (Project 129034), VIEP–BUAP (GOMM–EXC10–I), PROMEP/103.5/07/2594 and CA Física Computacional de la Materia Condensada. J.A. thanks Conacyt (Project 81667) for financial support and to Laboratorio de Supercómputo for time allo-cation. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Phase equilibria and interfacial properties of two-dimensional Yukawa fluids Фазова рiвновага i мiжфазнi властивостi двовимiрних Юкава-плинiв Article published earlier |
| spellingShingle | Phase equilibria and interfacial properties of two-dimensional Yukawa fluids Méndez-Maldonado, G.A. González-Melchor, M. Alejandre, J. |
| title | Phase equilibria and interfacial properties of two-dimensional Yukawa fluids |
| title_alt | Фазова рiвновага i мiжфазнi властивостi двовимiрних Юкава-плинiв |
| title_full | Phase equilibria and interfacial properties of two-dimensional Yukawa fluids |
| title_fullStr | Phase equilibria and interfacial properties of two-dimensional Yukawa fluids |
| title_full_unstemmed | Phase equilibria and interfacial properties of two-dimensional Yukawa fluids |
| title_short | Phase equilibria and interfacial properties of two-dimensional Yukawa fluids |
| title_sort | phase equilibria and interfacial properties of two-dimensional yukawa fluids |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/120270 |
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