Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer
Grand canonical Monte Carlo simulation results are reported for an electric double layer modelled by a planar charged hard wall, anisotropic shape cations, and spherical anions at different electrolyte concentrations and asymmetric valencies. The cations consist of two tangentially tethered hard sph...
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Інститут фізики конденсованих систем НАН України
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irk-123456789-1557882019-06-18T01:28:09Z Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer Kaja, M. Lamperski, S. Silvestre-Alcantara, W. Bhuiyan, L.B. Henderson, D. Grand canonical Monte Carlo simulation results are reported for an electric double layer modelled by a planar charged hard wall, anisotropic shape cations, and spherical anions at different electrolyte concentrations and asymmetric valencies. The cations consist of two tangentially tethered hard spheres of the same diameter, d. One sphere is charged while the other is neutral. Spherical anions are charged hard spheres of diameter d. The ion valency asymmetry 1:2 and 2:1 is considered, with the ions being immersed in a solvent mimicked by a continuum dielectric medium at standard temperature. The simulations are carried out for the following electrolyte concentrations: 0.1, 1.0 and 2.0 M. Profiles of the electrode-ion, electrode-neutral sphere singlet distributions, the average orientation of dimers, and the mean electrostatic potential are calculated for a given electrode surface charge, σ, while the contact electrode potential and the differential capacitance are presented for varying electrode charge. With an increasing electrolyte concentration, the shape of differential capacitance curve changes from that with a minimum surrounded by maxima into that of a distorted single maximum. For a 2:1 electrolyte, the maximum is located at a small negative σ value while for 1:2, at a small positive value. Представлено результати моделювання Монте Карло симуляцiй у великому канонiчному ансамблi для електричного подвiйного шару поблизу плоскої зарядженої твердої поверхнi, який складається з катiонiв анiзотропної форми та сферичних анiонiв при рiзних концентрацiях електролiту та для випадку асиметричної валентностi. Катiони складаються з двох тангенцiйно зв’язаних твердих сфер однакового дiаметру d. Одна сфера є зарядженою, а друга — нейтральною. Сферичнi анiони — це зарядженi твердi сфери дiаметру d. Розглядається асиметрiя iонної валентностi 1:2 i 2:1, причому iони знаходяться у розчиннику як дiелектричне середовище при нормальнiй температурi. Симуляцiї здiйснювалися при концентрацiї електролiту: 0.1, 1.0 i 2.0 M. Профiлi розподiлiв електрод-iон, електрод-нейтральна сфера, середня концентрацiя димерiв i середнiй електростатичний потенцiал обчисленi при фiксованому поверхневому зарядi σ, в той час як контактний потенцiал електроду i диференцiйна ємнiсть представленi при зарядi електроду, який змiнюється. При збiльшеннi концентрацiї електролiта крива диференцiйної ємностi змiнюється вiд мiнiмуму, оточеного максимумами, до форми iз спотвореним єдиним максимумом. Для електролiту 2:1, максимум розташований при невеликому вiд’ємному зарядi, в той час як для електролiта 1:2 — при невеликому позитивному значеннi заряду. 2016 Article Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer / M. Kaja, S. Lamperski, W. Silvestre-Alcantara, L.B. Bhuiyan, D. Henderson // Condensed Matter Physics. — 2016. — Т. 19, № 1. — С. 13804: 1–10 . — Бібліогр.: 39 назв. — англ. 1607-324X DOI:10.5488/CMP.19.13804 arXiv:1603.02445 PACS: 82.45.Fk, 61.20.Qg, 73.30.+y, 82.45.Mp, 61.20.Ja http://dspace.nbuv.gov.ua/handle/123456789/155788 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
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Grand canonical Monte Carlo simulation results are reported for an electric double layer modelled by a planar charged hard wall, anisotropic shape cations, and spherical anions at different electrolyte concentrations and asymmetric valencies. The cations consist of two tangentially tethered hard spheres of the same diameter, d. One sphere is charged while the other is neutral. Spherical anions are charged hard spheres of diameter d. The ion valency asymmetry 1:2 and 2:1 is considered, with the ions being immersed in a solvent mimicked by a continuum dielectric medium at standard temperature. The simulations are carried out for the following electrolyte concentrations: 0.1, 1.0 and 2.0 M. Profiles of the electrode-ion, electrode-neutral sphere singlet distributions, the average orientation of dimers, and the mean electrostatic potential are calculated for a given electrode surface charge, σ, while the contact electrode potential and the differential capacitance are presented for varying electrode charge. With an increasing electrolyte concentration, the shape of differential capacitance curve changes from that with a minimum surrounded by maxima into that of a distorted single maximum. For a 2:1 electrolyte, the maximum is located at a small negative σ value while for 1:2, at a small positive value. |
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Article |
| author |
Kaja, M. Lamperski, S. Silvestre-Alcantara, W. Bhuiyan, L.B. Henderson, D. |
| spellingShingle |
Kaja, M. Lamperski, S. Silvestre-Alcantara, W. Bhuiyan, L.B. Henderson, D. Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer Condensed Matter Physics |
| author_facet |
Kaja, M. Lamperski, S. Silvestre-Alcantara, W. Bhuiyan, L.B. Henderson, D. |
| author_sort |
Kaja, M. |
| title |
Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer |
| title_short |
Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer |
| title_full |
Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer |
| title_fullStr |
Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer |
| title_full_unstemmed |
Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer |
| title_sort |
influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer |
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Інститут фізики конденсованих систем НАН України |
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2016 |
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http://dspace.nbuv.gov.ua/handle/123456789/155788 |
| citation_txt |
Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer / M. Kaja, S. Lamperski, W. Silvestre-Alcantara, L.B. Bhuiyan, D. Henderson // Condensed Matter Physics. — 2016. — Т. 19, № 1. — С. 13804: 1–10
. — Бібліогр.: 39 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
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2025-07-14T08:01:28Z |
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2025-07-14T08:01:28Z |
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1837608561514905600 |
| fulltext |
Condensed Matter Physics, 2016, Vol. 19, No 1, 13804: 1–10
DOI: 10.5488/CMP.19.13804
http://www.icmp.lviv.ua/journal
Influence of anisotropic ion shape, asymmetric
valency, and electrolyte concentration on structural
and thermodynamic properties of an electric
double layer
M. Kaja1, S. Lamperski1∗, W. Silvestre-Alcantara2, L.B. Bhuiyan2, D. Henderson3
1 Department of Physical Chemistry, Adam Mickiewicz University of Poznań,
Umultowska 89b, 61-614 Poznań, Poland
2 Laboratory of Theoretical Physics, Department of Physics, University of Puerto Rico,
San Juan, 00931-3343, Puerto Rico
3 Department of Chemistry and Biochemistry, Brigham Young University, Provo UT 84602-5700, USA
Received November 20, 2015, in final form January 12, 2016
Grand canonical Monte Carlo simulation results are reported for an electric double layer modelled by a planar
charged hard wall, anisotropic shape cations, and spherical anions at different electrolyte concentrations and
asymmetric valencies. The cations consist of two tangentially tethered hard spheres of the same diameter, d .
One sphere is charged while the other is neutral. Spherical anions are charged hard spheres of diameter d .
The ion valency asymmetry 1:2 and 2:1 is considered, with the ions being immersed in a solvent mimicked
by a continuum dielectric medium at standard temperature. The simulations are carried out for the following
electrolyte concentrations: 0.1, 1.0 and 2.0 M. Profiles of the electrode-ion, electrode-neutral sphere singlet
distributions, the average orientation of dimers, and the mean electrostatic potential are calculated for a given
electrode surface charge,σ, while the contact electrode potential and the differential capacitance are presented
for varying electrode charge. With an increasing electrolyte concentration, the shape of differential capacitance
curve changes from that with a minimum surrounded by maxima into that of a distorted single maximum. For
a 2:1 electrolyte, the maximum is located at a small negative σ value while for 1:2, at a small positive value.
Key words: charged dimers, valency asymmetry, electrical double layer, grand-canonical Monte Carlo
simulation
PACS: 82.45.Fk, 61.20.Qg, 73.30.+y, 82.45.Mp, 61.20.Ja
This article is dedicated to Professor Stefan Sokołowski, the famous Polish scientist and our friend, on
the occasion of his 65th birthday.
1. Introduction
Development of the electrical double layer (EDL) theory as well as the progress in the numerical
technology have resulted in proposition and examination of an increasing number of EDL models. The
Gouy-Chapman theory (GC) [1, 2] is based on solving the Poisson-Boltzmann equation and applies a mean
field approximation to describe the electrostatic interactions. The GC theory can be applied to the sim-
plest model of an electrolyte, which does not take into account the volume of ions. In this model, ions
are represented by point electric charges, and the solvent is a dielectric continuum with the relative per-
mittivity εr. It is worth noting that the Debye-Hückel theory uses the same model of an electrolyte. The
∗E-mail: slamper@amu.edu.pl
©M. Kaja, S. Lamperski, W. Silvestre-Alcantara, L.B. Bhuiyan, D. Henderson, 2016 13804-1
http://dx.doi.org/10.5488/CMP.19.13804
http://www.icmp.lviv.ua/journal
M. Kaja et al.
GC theory describes well low density electrolytes at small electrode charges. It breaks down at higher
concentrations and charges because the excluded volume and correlation effects are disregarded.
The hard-sphere and electrostatic correlation effects are considered in modern theories of EDL such
as the Modified Poisson-Boltzmann Theory (MPB) [3, 4], the Mean Spherical Approximation (MSA) [5], the
Hypernetted Chain Theory (HNC) [6, 7] or more recently the Density Functional Theory (DFT) [8]. They
have been used to describe the primitive model of an electrolyte (PM) [9] and the restricted primitive
model (RPM) [10]. In the PM model, ions are represented by hard spheres of different diameters with
a point electric charge located at the centre. The charged spheres are immersed in a medium with the
relative permittivity εr characteristic of a solvent. In the RPMmodel, the ion diameters are the same. ForEDL composed of a planar electrode and a PM or RPM electrolyte, the modern theories predict the layer-
ing effect at high absolute values of the electrode charges [11, 12] and the transition of the capacitance
minimum into a maximum at small electrode charges caused by an increasing electrolyte concentration
[4]. The GC theory fails to describe these effects.
Due to correlation effects that are included, the MPB and DFT theories have been successfully applied
to the solvent primitive model (SPM) electrolyte. SPM is the simplest model of an electrolyte which in-
cludes the volume of solvent molecules. In SPM, solvent molecules are modelled by neutral hard spheres
whose diameter is the same as [13, 14] or different [15] from that of ions. Neutral spheres as well as
cations and anions are immersed in the continuous dielectric medium characterised by εr. The presenceof neutral spheres leads to the generation of density oscillations near the electrode surface and to an
increase in the differential capacitance of EDL [16].
Of the formal statistical mechanical theories, the HNC has been applied to the non-primitive model
(NP) [17] in which solvent molecules aremodelled by hard spheres with a point permanent electric dipole
moment located at the centre. However, it leads to lowered values of the relative permittivity.
The DFT theory gives fresh possibilities. Due to the free energy term of intra-molecular interactions,
the DFT theory is applicable to ions of more complicated topology than spherical. Here, we must mention
the work by Sokołowski [18] who has applied the modified DFT theory to the study of orientation or-
dering of electrostatic neutral hard dumbbells at the planar surface. Charged dumbbells, called dimers,
have aroused great interest in investigation of the EDL properties [19, 20]. This advanced model of an
electrolyte has been used for modelling systems of high densities like ionic liquids [21].
Torrie and Valleau [10] have introduced the computer simulation technique into the investigation
of EDL. At that time computer simulation results were used to confirm the correctness of EDL theories.
Now, the tremendous development of numerical technology has opened new area of application inacces-
sible for theory. Fedorov et al. [22] have studied models of ionic liquids made of one, two or three beads,
assuming that one of the hard spheres in the chain had a positive charge. Breitsprecher et al. [23, 24]
have conducted molecular dynamics simulations for ions with different size and valency, represented
by a coarse-grained model. Silvestre-Alcantara et al. [25] have investigated the properties of ELD con-
taining fused dimer electrolyte. Charged hard walls and hard spheres have been replaced by molecular
electrodes and soft sphere ions [26–28]. Ions of topology characteristic of ionic liquids are investigated.
The solvent is no longer a dielectric continuum but is modelled by explicit molecular models [29]. Thus,
the present models of EDL have become more realistic.
Recently, we have intensively investigated the EDL containing a dimer electrolyte. Among other ef-
fects, we have analysed the influence of concentration of 1:1 electrolyte [21] and of ion valence asym-
metries [30] of charged dimers on the properties of EDL. However, we did not consider the properties
of EDL for asymmetric ion valencies at different electrolyte concentrations. In particular, we expect new
shapes of the differential capacitance. Thus, in this paper, we discuss the influence of anisotropic ion
shape on the structural and thermodynamic properties of ELD containing asymmeteric 2:1 and 1:2 dimer
electrolytes of different concentrations.
2. Model and methods
The electric double layer is composed of a planar electrode and an electrolyte, which is a mixture of
spherical anions and anisotropic cations in the shape of dimers. The dimer consists of two tangentially
tethered hard spheres, one of which has a point electric charge immersed at the centre and the other is
13804-2
Anisotropic ion shape
neutral. The diameters of the two spheres of a dimer and the sphere of a monomer anion are the same.
The ion valencies are asymmetric with the ions being immersed in a homogeneousmedium of the relative
permittivity, εr. The electrode is modelled by a hard planar wall with a uniformly distributed charge ofsurface density, σ. The image effect is not considered which means that εr of the electrode material andsolvent are the same. The ion-ion and electrode-ion interactions are given by
ui j (r ) =
{ ∞, r < (di +d j )/2,
1
4πε0εr
e2 Zi Z j
r , r Ê (di +d j )/2,
(1)
and
uwi (x) =
{
∞, x < d/2,
−σZs ex
ε0εr , x Ê d/2,
(2)
respectively. Here, e is the magnitude of the elementary charge, and Zs is the valency of the particle ofspecies s. Also, ε0 is the vacuum permittivity, r is the separation between the centres of the two hard
spheres, and x is the perpendicular distance from the electrode surface to the centre of a hard sphere.
The local number density ρs (x) of the species s at a distance x is the first average quantity obtained
from our simulations. The reduced local density or the singlet distribution function gs (x) = ρs (x)/ρ0
s ,(ρ0
s is the corresponding bulk number density) is used to describe the structure of ELD. Also, the meanelectrostatic potential ψ(x) is defined in terms of ρs (x)
ψ(x) = e
ε0εr
∑
s
Zs
∞∫
x
ρs (x ′)(x −x ′)dx ′. (3)
The differential capacitanceCd is the property which can be compared with the experimental results.The differential capacity is defined as
Cd = dσ/dψ(0). (4)
In practice, Cd was calculated from the interpolation polynomials method introduced by Lamperski andZydor [31].
The local (volume) charge density ρQ (x)
ρQ (x) =∑
s
Zs egs (x) (5)
and the local net charge per unit area, σΣ(x)
σΣ(x) =σ+
x∫
0
ρQ (x ′)dx ′ (6)
are the properties that can be used for indicating the charge inversion (CI) and charge reversal (CR)
phenomena. The CI effect takes place when the electrode charge and the charge density of the second
layer and, less commonly, subsequent layers of ions next to the electrode are of the same sign. When the
charge of the first layer of counter-ions overcomes the charge of an electrode, the electric field reverses its
direction. The functionσΣ(x) has the sign opposite to that ofσ. This effect is called the charge reversal [32,
33]. Essentially at some x, the integrated charge overcompensates or overscreens the electrode charge.
Hence, the often used term charge overscreening occurs in the literature.
The second average quantity obtained from our simulations is the mean orientation function 〈cosθ〉.
It depends on the distance x from the electrode surface. The function 〈cosθ〉 is the average value of cosθ,
where θ is the angle between the normal to the electrode surface and the straight line joining the centres
of hard spheres constituting a dimer. The origin is located at the centre of the charged sphere.
The GCMC technique was applied to calculate the local densities, ρs (x), and orientation 〈cosθ〉 pro-
files. This technique is recommended for inhomogeneous systems [34] as it eliminates difficulties associ-
ated with the determination of the bulk concentration which appears when MC simulations are carried
out in the canonical ensemble. The details of the GCMC technique and its implementation to our investi-
gation have been described in the previous papers [4, 35]. The procedure FLIP3 [36] was used to rotate the
dimer while the long-range electrostatic interactions were estimated with the method proposed by Torrie
and Valleau [10]. The ionic activity coefficients required by the GCMC technique as input were obtained
from the inverse GCMC method [37].
13804-3
M. Kaja et al.
3. Results
Simulations were carried out for the asymmetric ion valencies 1:2 and 2:1 at three electrolyte concen-
trations 0.1, 1.0, and 2.0 M in the range of the electrode surface charges varying from −1.0 to +1.0 C m−2.
Diameters of positively charged and neutral spheres of dimers and of spherical anions are equal to
d = 425 pm. The other physical parameters were temperature T = 298.15 K, and the relative permit-
tivity of water, εr = 78.5. Because of the anisotropic shape of cations, the simulations were expected to
require significantly longer configurational sampling. We sampled 2 billion configurations to obtain high
precision averages.
Figure 1 shows the singlet distribution profiles of charged dimers and spherical anions for three elec-
trolyte concentrations 0.1, 1.0 and 2.0 M at σ = −0.30 C m−2. At this σ, a strong adsorption of dimers
is observed, while anions are repelled from the vicinity of the electrode surface. By contrast, at positive
values of σ, the adsorption of spherical anions occurs and now the dimer cations are repelled from the
electrode. As a result, the internal structure of the distant cation has little influence on the double layer
structure with the dimer behaving like a spherical ion (see for example, reference [30]). The surface prop-
erties of spherical ions are well known, so we do not discuss them here. The upper panel of figure 1 shows
the results for the 1:2 electrolyte, while the lower one for the 2:1 case. The density profiles of charged
spheres are similar to those observed for spherical counter-ions. A sharp peak corresponds to the contact
distance, d/2. As expected, its height decreases with an increasing electrolyte concentration. The peak
is higher and thinner for di-valent dimers as we have observed earlier [30]. The influence of a neutral
sphere is hardly visible. The neutral sphere density profiles have two maxima. The first corresponds to
the contact distance while the second is at x/d ≈ 1.45. The height of the second maximum relative to
the height of the first one increases with a decreasing electrolyte concentration. The first maximum in-
dicates that the large fraction of dimers take parallel orientation to the electrode surface. Assuming the
perpendicular orientation of a dimer with charged sphere adjacent the electrode surface, the centre of
the neutral sphere is located at x/d = 1.5. A good agreement of this prediction with the simulation results
Figure 1. (Color online) Dependence of the singlet distribution function, g (x), of charged dimers and
spherical anions (see also the insets) on the distance, x/d , from the electrode at the surface charge σ =
−0.3 C m−2 for electrolyte concentrations 0.10 M (triangles), 1.00 M (circles) and 2.00 M (squares) for ion
valencies 1:2 (upper panel) and 2:1 (lower panel). Empty symbols show the results for charged spheres,
filled for the neutral spheres of dimers and crossed for anions.
13804-4
Anisotropic ion shape
Figure 2. (Color online) Dependence of the angular orientation function, 〈cosθ〉, of dimers on the distance,
x/d . Parameters and symbols have the same meaning as in figure 1.
indicates that the perpendicular orientation is also very probable and its probability increases with a
decreasing electrolyte concentration. This conclusion confirms the mean orientation 〈cosθ〉 results.
The mean orientation 〈cosθ〉 profiles are shown in figure 2. The positive values of 〈cosθ〉 mean that
dimers prefer the orientation with the charged sphere towards the electrode. The function 〈cosθ〉 has
a nearly linear course from the contact distance to the position of the second maximum on the neutral
sphere density profile. At this position, the 〈cosθ〉 function has a minimum. The minimum is negative for
higher electrolyte concentrations and larger dimer valencies. At longer distances, the minimum trans-
forms into a positive maximum. After leaving the maximum, the 〈cosθ〉 function tends to zero and the
orientation randomisation takes place. Thus, the behaviour of 〈cosθ〉 suggests a generally perpendicular
orientation of the dimers near the electrode with the charged head nearer to it than the neutral tail, a
pattern that is consistent with our earlier studies. The contact values of 〈cosθ〉 are nearly independent of
the dimer valency, but at some distance from the electrode surface they are lower for the divalent dimers.
However, the course of curves remains similar. In the vicinity of the electrode surface, the rotation of the
neutral sphere around the charged one is hindered mainly by the hard wall of the electrode. The wall ef-
fect is independent of electrolyte concentration. The value of 〈cosθ〉 varies from 0.5 at a contact distance
to 0 at x/d = 1.5. The simulation contact results oscillate at around 0.5. They are greater than 0.5 for
c = 0.1M and lower than 0.5 for c = 2.0M. It means that, as we have stated earlier, the low concentration
electrolytes support the perpendicular orientation, while the electrolytes of high concentration enhance
the parallel one. In this range of distances, the rotation of the neutral sphere around the charged one is
hindered by steric and electrostatic interactions with neighbouring ions, only. The second maximum of
〈cosθ〉 shows that dimers form the second layer have their charged spheres oriented towards the elec-
trode. It is worth noting that this layer is not visible at the charged sphere density distributions for c = 1.0
and 2.0 M.
Most of the anion distribution functions shown in figure 1 have a small maximum at x/d > 1.5 (see
the insets). This maximum suggests the onset of the CI and CR phenomena. As a case in point, we have
calculated the profiles of the local charge density, ρQ (x), and the local net charge per unit area, σΣ(x),
which are presented in figure 3. It is seen that except the curve for the 1:2 electrolyte at concentration
c = 0.1M, which is monotonous, the remaining curves are all non-monotonous indicating the occurrence
13804-5
M. Kaja et al.
Figure 3. (Color online) Dependence of the local (volume) charge density ρQ (x) (filled symbols) and the
local net charge per unit area, σΣ(x) (empty symbols) on the distance, x/d . Parameters and symbols have
the same meaning as in figure 1.
of the CI and CR phenomena. The increase in electrolyte concentration or the presence of a higher valency
counterion intensifies these features. Indeed, at the same electrolyte concentration, the effect is more
pronounced for the 2:1 system than for the 1:2 system. The CI effect is observed closer to the electrode
surface than to the CR one. The mechanism of CI and CR is not completely clear [33].
The mean electrostatic potential profiles calculated from equation (3) are presented in figure 4. For
Figure 4. (Color online) Mean electrostatic potential ψ as a function of distance, x/d . Parameters and
symbols have the same meaning as in figure 1.
13804-6
Anisotropic ion shape
Figure 5. (Color online)Mean electrostatic potential of the electrode,ψ0 as a function of the surface chargedensity, σ. Symbols have the same meaning as in figure 1.
the 1:2 electrolyte at c = 0.1 and 1.0 M, the potential is negative and the curves do not have any extrema.
The remaining curves have a positive maximum characteristic of divalent electrolytes [38]. This maxi-
mum is related to the the CI effect. With an increasing electrolyte concentration and dimer valency, the
absolute value of the mean potential and the width of EDL decrease.
The dependence of the mean electrostatic potential of the electrode, ψ(0), on the electrode charge
Figure 6. (Color online) Differential capacitance, Cd , of the electrical double layer as a function of thesurface charge density, σ. Symbols have the same meaning as in figure 1.
13804-7
M. Kaja et al.
density σ calculated for the investigated electrolyte concentrations and on ion valencies is shown in
figure 5. The curves intersect in the vicinity of σ = 0. The slope of the curves in the range of adsorption
of divalent ions is smaller than in the range of adsorption of monovalent ones. The ψ(0) results are used
for the calculation of the differential capacitance of EDL.
Figure 6 shows the dependence of the differential capacitance, Cd, of EDL on the electrode chargedensity calculated for different asymmetric valencies and electrolyte concentrations. For c = 0.1M, theCdcurves have aminimum corresponding toσ≈ 0 and surrounded by two asymmetricmaxima. An increase
in the electrolyte concentration to c = 2.0M transforms the minimum into a distorted maximum. For the
1:2 electrolyte, the maximum is located at a positive σ, while for the 2:1 electrolyte, at a negative σ value.
The Gouy-Chapman theory [1, 2] predicts that the differential capacitance curve of EDL has the parabola-
like shape with a minimum at σ = 0. Transition of the capacitance curve from that having a minimum
to that having a maximum with an increasing electrolyte concentration has been explained for the RPM
electrolyte by an increase in the thickness of EDL due to the formation of bi- or multi-layer structures
of counterions [13, 39]. In the case of charged dimers, the increase in thickness of EDL is additionally
caused by the neutral spheres of dimers which separate the two layers of charged spheres: adsorbed on
the electrode surface and form the second layer. Finally, the increase in valency of counterions makes
the EDL thinner. Explanation of the behaviour of Cd−σ curve shown in figure 6 requires consideration
of all these effects.
4. Conclusions
A charged dimer is a simple and useful model of molecules of charged surfactants and ionic liquids.
Charged surfactants are composed of a charged head and a neutral, hydrophobic tail. In a charged dimer,
the head is represented by a charged sphere while the tail by a neutral one. Surfactants are diluted in
a solvent (water). Therefore, more advanced investigation of surfactants modelled by a charged dimer
should include solvent molecules. The interaction of the charged head and the neutral tail with molecules
of solvent depends strongly on the structural and polar properties of solvent molecules. Presumably they
can influence the density and orientation profiles. Ionic liquids are solvent freemolten crystals composed
of large organic ions with the electric charge located off the centre of the ion. Charged dimers can model
ionic liquids when their size is large and the concentration high. Current investigation of EDL composed
of ionic liquids as an electrolyte is extremely interesting. However, the investigation of EDL formed by
charged dimers by themethod ofmolecular simulations breaks down because of high density of a system.
The problem can be solved by replacing hard potentials with soft ones.
In this paper we have investigated the structural and thermodynamic properties of an electric double
layer composed of a planar charged hard wall, charged dimers and spherical anions at different elec-
trolyte concentrations and asymmetric ion valencies, using the grand canonical Monte Carlo simulation.
The density profiles of neutral spheres have two maxima corresponding to parallel and perpendicular
orientations of the dimer against the electrode surface. The height of the secondmaximum relative to the
height of the first one increases with a decreasing electrolyte concentration. Thus, we have concluded that
the probability of the perpendicular orientation increases with a decreasing electrolyte concentration.
The variation in the electrolyte concentration and ion valency leads to a diversity of shapes of differ-
ential capacitance curves. At low concentrations, the capacitance curves have a minimum surrounded
by two asymmetric maxima. With increasing concentrations, the minimum transforms into a distorted
maximum. For the 1:2 electrolyte, the maximum is located at positive σ, while for the 2:1 electrolyte, at a
negative σ value.
Acknowledgements
Monika Kaja and Stanisław Lamperski acknowledge the financial support from the Faculty of Chem-
istry, Adam Micklewicz University of Poznań.
13804-8
Anisotropic ion shape
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13804-9
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M. Kaja et al.
Вплив анiзотропної форми iонiв, асиметрiї валентностi та
концентрацiї електролiту на структурнi i термодинамiчнi
властивостi електричного подвiйного шару
M. Кайя1, С. Ламперский1, В. Сильвестр-Алькантара2, Л.Б. Буян2, Д. Гендерсон3
1 Вiддiл фiзичної хiмiї, Унiверситет Адама Мiцкевича в Познанi, Познань, Польща
2 Лабораторiя теоретичної фiзики, фiзичний факультет Унiверситету Пуерто Рiко, Пуерто Рiко
3 Факультет хiмiї та бiохiмiї, Унiверситет Бригама Янга, Прово, США
Представлено результати моделювання Монте Карло симуляцiй у великому канонiчному ансамблi для
електричного подвiйного шару поблизу плоскої зарядженої твердої поверхнi, який складається з катiонiв
анiзотропної форми та сферичних анiонiв при рiзних концентрацiях електролiту та для випадку асиме-
тричної валентностi. Катiони складаються з двох тангенцiйно зв’язаних твердих сфер однакового дiаме-
тру d . Одна сфера є зарядженою, а друга— нейтральною. Сферичнi анiони— це зарядженi твердi сфери
дiаметру d . Розглядається асиметрiя iонної валентностi 1:2 i 2:1, причому iони знаходяться у розчинни-
ку як дiелектричне середовище при нормальнiй температурi. Симуляцiї здiйснювалися при концентрацiї
електролiту: 0.1, 1.0 i 2.0 M. Профiлi розподiлiв електрод-iон, електрод-нейтральна сфера, середня концен-
трацiя димерiв i середнiй електростатичний потенцiал обчисленi при фiксованому поверхневому зарядi
σ, в той час як контактний потенцiал електроду i диференцiйна ємнiсть представленi при зарядi електро-
ду, який змiнюється. При збiльшеннi концентрацiї електролiта крива диференцiйної ємностi змiнюється
вiд мiнiмуму, оточеного максимумами, до форми iз спотвореним єдиним максимумом. Для електролiту
2:1, максимум розташований при невеликому вiд’ємному зарядi, в той час як для електролiта 1:2— при
невеликому позитивному значеннi заряду.
Ключовi слова: зарядженi димери, асиметрiя валентностi, електричний подвiйний шар,Монте Карло
моделювання у великому канонiчному ансамблi
13804-10
Introduction
Model and methods
Results
Conclusions
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