Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer

W2295851084 · 수집 2026-10-04 18:12:24

T12274 Electrostatics and Colloid Interactions

CoT 라벨링

라벨링 전

PDF 파일

자동 다운로드한 PDF PDF 보기

기본 정보

DOI 제목 발행년도 저널 URL 페이지 열기 PDF URL PDF 열기 발행기관 피인용수 라이선스

추가 정보 초록

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.

본문

Condensed Matter Physics, 2016, Vol. 19, No 1, 13804: 1–10

[DOI: 10.5488/CMP.19.13804](http://dx.doi.org/10.5488/CMP.19.13804)

[http://www.icmp.lviv.ua/journal](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. Kaja 1, S. Lamperski 1 _∗_, W. Silvestre-Alcantara 2, L.B. Bhuiyan 2, D. Henderson 3

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 permittivity _ϵ_ r. 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 _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 _ϵ_ r characteristic of a solvent. In the RPM model, the ion diameters are the same. For

EDL 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 _ϵ_ r. The presence

of 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 are modelled 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 homogeneous medium of the relative
permittivity, _ϵ_ r. The electrode is modelled by a hard planar wall with a uniformly distributed charge of
surface density, _σ_ . The image effect is not considered which means that _ϵ_ r of the electrode material and

solvent are the same. The ion-ion and electrode-ion interactions are given by

(1)

_ui j_ ( _r_ ) _=_

- _∞_, _r_ _<_ ( _di +_ _d j_ )/2,

1
4 _πϵ_ 0 _ϵ_ r

_r_, _r_ _�_ ( _di +_ _d j_ )/2,

_e_ 2 _Zi_ _Z_ _j_

and

_uwi_ ( _x_ ) _=_

- _∞_, _x < d_ /2,

_−_ _σ_ _ϵ_ _Z_ 0 _s_ _ϵ_ _ex_ r , _x �_ _d_ /2, (2)

respectively. Here, _e_ is the magnitude of the elementary charge, and _Zs_ is the valency of the particle of
species _s_ . Also, _ϵ_ 0 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 _g_ _s_ ( _x_ ) _= ρs_ ( _x_ )/ _ρ_ 0 _s_ ,

( _ρ_ 0 _s_ is the corresponding bulk number density) is used to describe the structure of ELD. Also, the mean

electrostatic potential _ψ_ ( _x_ ) is defined in terms of _ρs_ ( _x_ )

_e_
_ψ_ ( _x_ ) _=_
_ϵ_ 0 _ϵ_ r

_s_

_∞_

_ρs_ ( _x_ _′_ )( _x −_ _x_ _′_ )d _x_ _′_ . (3)

_∞_

_x_

_Zs_

The differential capacitance _C_ d is the property which can be compared with the experimental results.

The differential capacity is defined as

_C_ d _=_ d _σ_ /d _ψ_ (0). (4)

In practice, _C_ d was calculated from the interpolation polynomials method introduced by Lamperski and

Zydor [31].

The local (volume) charge density _ρQ_ ( _x_ )

_ρQ_ ( _x_ ) _=_
_s_

and the local net charge per unit area, _σ_ Σ( _x_ )

_Zs_ _eg_ _s_ ( _x_ ) (5)

_x_

_σ_ Σ( _x_ ) _= σ_ _+_

_ρQ_ ( _x_ _′_ )d _x_ _′_ (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 function _σ_ Σ( _x_ ) has the sign opposite to that of _σ_ . 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 _〈_ cos _θ〉_ .
It depends on the distance _x_ from the electrode surface. The function _〈_ cos _θ〉_ is the average value of cos _θ_,
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 _〈_ cos _θ〉_ profiles. 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 concentrations 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 permittivity of water, _ϵ_ r _=_ 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 electrolyte 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, _〈_ cos _θ〉_, 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 _〈_ cos _θ〉_ results.

The mean orientation _〈_ cos _θ〉_ profiles are shown in figure 2. The positive values of _〈_ cos _θ〉_ mean that
dimers prefer the orientation with the charged sphere towards the electrode. The function _〈_ cos _θ〉_ 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 _〈_ cos _θ〉_ function has a minimum. The minimum is negative for

higher electrolyte concentrations and larger dimer valencies. At longer distances, the minimum transforms into a positive maximum. After leaving the maximum, the _〈_ cos _θ〉_ function tends to zero and the
orientation randomisation takes place. Thus, the behaviour of _〈_ cos _θ〉_ 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 _〈_ cos _θ〉_ 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 effect is independent of electrolyte concentration. The value of _〈_ cos _θ〉_ 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 =_ 0.1 M and lower than 0.5 for _c =_ 2.0 M. 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
_〈_ cos _θ〉_ shows that dimers form the second layer have their charged spheres oriented towards the electrode. 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, _σ_ Σ( _x_ ),
which are presented in figure 3. It is seen that except the curve for the 1:2 electrolyte at concentration

_c =_ 0.1 M, 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, _σ_ Σ( _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, _ψ_ 0 as a function of the surface charge
density, _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 the
surface 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, _C_ d, of EDL on the electrode charge
density calculated for different asymmetric valencies and electrolyte concentrations. For _c =_ 0.1 M, the _C_ d
curves have a minimum corresponding to _σ ≈_ 0 and surrounded by two asymmetric maxima. An increase
in the electrolyte concentration to _c =_ 2.0 M 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 parabolalike 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 _C_ d _−_ _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 free molten 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 the method of molecular 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 second maximum 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

References

1. Gouy M., J. Phys. (Paris), 1910, 9 [, 457; doi:10.1051/jphystap:019100090045700.](http://dx.doi.org/10.1051/jphystap:019100090045700)

2. Chapman D.L., Philos. Mag., 1913, 25 [, 475; doi:10.1080/14786440408634187.](http://dx.doi.org/10.1080/14786440408634187)

3. Outhwaite C.W., Bhuiyan L.B., Levine S., J. Chem. Soc., Faraday Trans. 2, 1980, 76, 1388;

[doi:10.1039/F29807601388.](http://dx.doi.org/10.1039/F29807601388)

4. Lamperski L., Outhwaite C.W., Bhuiyan L.B., J. Phys. Chem. B, 2009, 113 [, 8925; doi:10.1021/jp900037h.](http://dx.doi.org/10.1021/jp900037h)

5. Henderson D., Lamperski S., Outhwaite C.W., Bhuiyan L.B., Collect. Czech. Chem. Commun., 2010, 75, 303;

[doi:10.1135/cccc2009094.](http://dx.doi.org/10.1135/cccc2009094)

6. Henderson D., Blum L., J. Electroanal. Chem., 1980, 111 [, 217; doi:10.1016/S0022-0728(80)80041-6.](http://dx.doi.org/10.1016/S0022-0728%0x2880%0x2980041-6)

7. Henderson D., Blum L., Smith W.R., Chem. Phys. Lett., 1979, 63 [, 381; doi:10.1016/0009-2614(79)87041-4.](http://dx.doi.org/10.1016/0009-2614%0x2879%0x2987041-4)

8. Pizio O., Sokołowski S., J. Chem. Phys., 2013, 138 [, 204715; doi:10.1063/1.4807777.](http://dx.doi.org/10.1063/1.4807777)

9. Bešter M., Vlachy V., J. Chem. Phys., 1992, 96 [, 7656; doi:10.1063/1.462366.](http://dx.doi.org/10.1063/1.462366)

10. Torrie G.M., Valleau J.P., J. Chem. Phys., 1980, 73 [, 5807; doi:10.1063/1.440065.](http://dx.doi.org/10.1063/1.440065)

11. Lamperski S., Bhuiyan L.B., J. Electroanal. Chem., 2003, 540 [, 79; doi:10.1016/S0022-0728(02)01278-0.](http://dx.doi.org/10.1016/S0022-0728%0x2802%0x2901278-0)

12. Zhou S., Lamperski S., Zydorczak M., J. Chem. Phys., 2014, 141 [, 064701; doi:10.1063/1.4892415.](http://dx.doi.org/10.1063/1.4892415)

13. Tang Z., Scriven L.E., Davis H.T., J. Chem. Phys., 1992, 97 [, 494; doi:10.1063/1.463595.](http://dx.doi.org/10.1063/1.463595)

14. Lamperski S., Outhwaite C.W., Bhuiyan L.B., Mol. Phys., 1996, 87 [, 1049; doi:10.1080/00268979600100721.](http://dx.doi.org/10.1080/00268979600100721)

15. Płuciennik M., Outhwaite C.W., Lamperski S., Mol. Phys., 2014, 112 [, 165; doi:10.1080/00268976.2013.805847.](http://dx.doi.org/10.1080/00268976.2013.805847)

16. Grimson M.J., Rickayzen G., Chem. Phys. Lett., 1982, 86 [, 71; doi:10.1016/0009-2614(82)83119-9.](http://dx.doi.org/10.1016/0009-2614%0x2882%0x2983119-9)

17. Outhwaite C.W., Lamperski S., Condens. Matter Phys., 2001, 4 [, 739; doi:10.5488/CMP.4.4.739.](http://dx.doi.org/10.5488/CMP.4.4.739)

18. Sokołowski S., J. Chem. Phys., 1991, 95 [, 7513; doi:10.1063/1.461377.](http://dx.doi.org/10.1063/1.461377)

19. Bhuiyan L.B., Lamperski S., Wu J., Henderson D., J. Phys. Chem. B, 2012, 116 [, 10364; doi:10.1021/jp304362y.](http://dx.doi.org/10.1021/jp304362y)

20. Lamperski S., Kaja M., Bhuiyan L.B., Wu J., Henderson D., J. Chem. Phys., 2013, 139, 054703;

[doi:10.1063/1.4817325.](http://dx.doi.org/10.1063/1.4817325)

21. Wu J., Jiang T., Jiang D., Jin Z., Henderson D., Soft Matter, 2011, 7 [, 11222; doi:10.1039/C1SM06089A.](http://dx.doi.org/10.1039/C1SM06089A)

22. Fedorov M.V., Georgi N., Kornyshev A.A., Electrochem. Commun., 2010, 12 [, 296; doi:10.1016/j.elecom.2009.12.019.](http://dx.doi.org/10.1016/j.elecom.2009.12.019)

23. Breitsprecher K., Košovan P., Holm C., J. Phys.: Condens. Matter, 2014, 26, 284108;

[doi:10.1088/0953-8984/26/28/284108.](http://dx.doi.org/10.1088/0953-8984/26/28/284108)

24. Breitsprecher K., Košovan P., Holm C., J. Phys.: Condens. Matter, 2014, 26, 284114;

[doi:10.1088/0953-8984/26/28/284114.](http://dx.doi.org/10.1088/0953-8984/26/28/284114)

25. Silvestre-Alcantara W., Kaja M., Henderson D., Lamperski S., Bhuiyan L.B., Mol. Phys., 2015, 114, 53;

[doi:10.1080/00268976.2015.1083132.](http://dx.doi.org/10.1080/00268976.2015.1083132)

26. Lanning O.J., Madden P.A., J. Chem. Phys. B, 2004, 108 [, 11069; doi:10.1021/jp048102p.](http://dx.doi.org/10.1021/jp048102p)

27. Górniak R., Lamperski S., J. Phys. Chem. C, 2014, 118 [, 3156; doi:10.1021/jp411698w.](http://dx.doi.org/10.1021/jp411698w)

28. Fedorov M.V., Kornyshev A.A., J. Phys. Chem. B, 2008, 112 [, 11868; doi:10.1021/jp803440q.](http://dx.doi.org/10.1021/jp803440q)

29. Předota M., Bandura A.V., Cummings P.T., Kubicki J.D., Wesolowski D.J., Chialvo A.A., Macheskyr M.L., J. Phys.

Chem. B, 2004, 108 [, 12049; doi:10.1021/jp037197c.](http://dx.doi.org/10.1021/jp037197c)

30. Kaja M., Silvestre-Alcantara W., Lamperski S., Henderson D., Bhuiyan L.B., Mol. Phys., 2015, 113, 1043;

[doi:10.1080/00268976.2014.968651.](http://dx.doi.org/10.1080/00268976.2014.968651)

31. Lamperski S., Zydor A., Electrochim. Acta, 2007, 52 [, 2429; doi:10.1016/j.electacta.2006.08.045.](http://dx.doi.org/10.1016/j.electacta.2006.08.045)

32. Chialvo A.A., Simonson J.M., Condens. Matter Phys., 2011, 14 [, 33002; doi:10.5488/CMP.14.33002.](http://dx.doi.org/10.5488/CMP.14.33002)

33. Jiménez-Ángeles F., Lozada-Cassou M., J. Phys. Chem. B, 2004, 108 [, 7286; doi:10.1021/jp036464b.](http://dx.doi.org/10.1021/jp036464b)

34. Frenkel D., Smit B., Understanding Molecular Simulation: From Algorithms to Applications, Academic Press, San

Diego 1996, p. 126.

35. Lamperski S., Outhwaite C.W., J. Colloid Interface Sci., 2008, 328 [, 458; doi:10.1016/j.jcis.2008.09.050.](http://dx.doi.org/10.1016/j.jcis.2008.09.050)

36. Allen M.P., Tildesley D.J., Computer Simulation of Liquids, Oxford University Press, Oxford, 1987, p. 349.

37. Lamperski S., Mol. Simul., 2007, 33 [, 1193; doi:10.1080/08927020701739493.](http://dx.doi.org/10.1080/08927020701739493)

38. Bhuiyan L.B., Outhwaite C.W., Phys. Chem. Chem. Phys., 2004, 6 [, 3467; doi:10.1039/b316098j.](http://dx.doi.org/10.1039/b316098j)

39. Lamperski S., Sosnowska J., Bhuiyan L.B., Henderson D., J. Chem. Phys., 2014, 140 [, 014704; doi:10.1063/1.4851456.](http://dx.doi.org/10.1063/1.4851456)

13804-9

M. Kaja _et al_ .

Вплив анiзотропної форми iонiв, асиметрiї валентностi та

концентрацiї електролiту на структурнi i термодинамiчнi

властивостi електричного подвiйного шару

M. Кайя 1, С. Ламперский 1, В. Сильвестр-Алькантара 2, Л.Б. Буян 2, Д. Гендерсон 3

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

본문 출처 PDF: PDF 보기 · 다른 PDF는 위 [PDF 업로드]로 올릴 수 있습니다.

활용가능성

이력 0건

아직 편집 이력이 없습니다. 저장할 때마다 이전 내용이 여기에 백업됩니다.