Some rigorous relations for partial conductivities in ionic liquids
Starting with the rigorous expressions, derived previously for the generalized transport coefficients of a multicomponent fluid, we obtained several exact relations for partial conductivities of ionic charge-asymmetric mixtures. For a simpler case of a charge-symmetric binary mixture such kind of re...
Збережено в:
| Опубліковано в: : | Condensed Matter Physics |
|---|---|
| Дата: | 2010 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2010
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/32129 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Some rigorous relations for partial conductivities in ionic liquids / I. Mryglod, V. Kuporov // Condensed Matter Physics. — 2010. — Т. 13, № 4. — С. 43602:1-8. — Бібліогр.: 10 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860078307180019712 |
|---|---|
| author | Mryglod, I. Kuporov, V. |
| author_facet | Mryglod, I. Kuporov, V. |
| citation_txt | Some rigorous relations for partial conductivities in ionic liquids / I. Mryglod, V. Kuporov // Condensed Matter Physics. — 2010. — Т. 13, № 4. — С. 43602:1-8. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| description | Starting with the rigorous expressions, derived previously for the generalized transport coefficients of a multicomponent fluid, we obtained several exact relations for partial conductivities of ionic charge-asymmetric mixtures. For a simpler case of a charge-symmetric binary mixture such kind of relations was discovered experimentally by Sundheim more than 50 years ago and is known as the “universal golden rule”. Some more complicate models, describing in particular the cases of ternary and multi-component mixtures, are considered. The general relation for partial ionic conductivities is derived for a multi-component ionic fluid. It is shown that such relations can be considered in fact as an example of a more general class of rigorous expressions valid for (k, ω)-dependent quantities.
|
| first_indexed | 2025-12-07T17:15:02Z |
| format | Article |
| fulltext |
Condensed Matter Physics 2010, Vol. 13, No 4, 43602: 1–8
http://www.icmp.lviv.ua/journal
Some rigorous relations for partial conductivities in
ionic liquids
I. Mryglod1,2, V. Kuporov1
1 Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine,
1 Svientsitskii Str., 79011 Lviv, Ukraine
2 Institute of Applied Mathematics and Fundamental Sciences of Lviv Polytechnic National University,
79013 Lviv, Ukraine
Received November 15, 2010
Starting with the rigorous expressions, derived previously for the generalized transport coefficients of a multi-
component fluid, we obtained several exact relations for partial conductivities of ionic charge-asymmetric
mixtures. For a simpler case of a charge-symmetric binary mixture such kind of relations was discovered
experimentally by Sundheim more than 50 years ago and is known as the “universal golden rule”. Some
more complicate models, describing in particular the cases of ternary and multi-component mixtures, are
considered. The general relation for partial ionic conductivities is derived for a multi-component ionic fluid. It
is shown that such relations can be considered in fact as an example of a more general class of rigorous
expressions valid for (k, ω)-dependent quantities.
Key words: Ionic liquids, transport coefficients, mutual diffusion coefficient, ionic conductivity, molten salt
PACS: 66.10.cg, 66.10.Ed, 82.45.Gj, 47.10.-g
Introduction
About 50 years ago a phenomenological “universal golden rule” for the ratio of partial conduc-
tivities of ions in molten salts was proposed by Sundheim [1] from the analysis of experimental
data. This rule is expressed in a very simple form
σ+
σ−
=
m−
m+
. (1)
Recently, there were made several theoretical attempts [2] to derive this relation using the equations
of motion, the Langevin equation as well as molecular dynamics studies for the model of binary
charge symmetrical molten salts. A few years later using similar approaches such relation was also
obtained for pseudo-binary molten salt KCl–NaCl [3].
Our goal is to consider this problem in a more general framework. We start with the rigorous
relations derived by us previously for generalized transport coefficients of a multi-component fluid
[4, 5]. We obtain the “universal golden rule” for (k, ω)-dependent partial conductivities of an ionic
charge-asymmetric binary mixture as well as the relations for the partial ionic conductivities in
some cases of ternary and four-component ionic liquids.
1. Theoretical framework
Let us start with some introductory remarks and consider the general framework that can
be used for the description of both kinds of multi-component mixtures, in particular mixtures of
neutral particles as well as mixtures containing charged particles. In general case we deal with a
ν-component fluid in the volume V , containing Nα particles in the αth species (α = 1, 2, . . . , ν).
To derive hydrodynamic equations one has to define the microscopic basic set of the slowest (hy-
drodynamic) variables [5], which for a multi-component mixture may be introduced as follows
c© I. Mryglod, V. Kuporov 43602-1
http://www.icmp.lviv.ua/journal
I. Mryglod, V. Kuporov
P̂ hyd
k
= {N̂k, Ĵk, Êk}, where N̂k = {N̂k,α} is a column-vector with the components
N̂k,α =
Nα
∑
i=1
exp{ikRα
i }, (2)
being the number density of particles in the α-th species; Ĵk is the density of the total current,
Ĵk =
∑
α
Ĵk,α , Ĵk,α =
Nα
∑
i=1
pα
i exp{ikRα
i }, (3)
with Ĵk,α being the current densities of particles in the α-th species, and
Êk =
∑
α
Êk,α =
∑
α
Nα
∑
i=1
eαi exp{ikRα
i } (4)
is the total energy density, where the one-particle energy eαj can be expressed via the sum of kinetic
energy and potential energy of pair interactions:
eαj =
[pα
j ]
2
2mα
+
∑
l 6=j,β
V βα
jl .
The set of dynamic variables P̂ hyd
k
= {N̂k, Ĵk, Êk} includes the densities of all the additive
integrals of motion for a mixture. In the case of longitudinal dynamics, as it follows from the sym-
metrical properties, the scalar densities n̂k,α and Êk interact only with the longitudinal component
of Ĵk, namely ĴL
k
, that is the projection of Ĵk onto the direction of wave-vector k. Hence, the total
number of longitudinal hydrodynamic variables for ν-component mixture is equal to ν+2, namely
P̂L
k
= {P̂ ι
k
} with ι = 1, 2, . . . , ν + 2.
In practical applications it may be more convenient [4, 5] to use the set of orthogonalized
dynamic variables possessing the following properties (P̂ ι
k
, P̂ κ
−k
) = δικ (P̂ ι
k
, P̂ κ
−k
). Such an orthog-
onalized set of longitudinal hydrodynamical variables can be defined as follows
P̂L
k = {N̂k, Ĵ
L
k , Ĥk} (5)
where
Ĥk = Êk − (Êk, N̂
+
k
)(N̂k, N̂
+
k
)−1N̂k = (1− PN )Êk
is the so-called enthalpy density, the Mori-like projection operator denotes as
PN . . . = (. . . ,N+
k
)(N̂k, N̂
+
k
)−1N̂ =
∑
αγ
(. . . , N̂−k,α) (N̂k, N̂
+
k
)−1
αγ N̂k,γ , (6)
and the notation (. . . , . . .) is used for the definition of an equilibrium correlation function
(A,B) = 〈(A− 〈A〉)(B − 〈B〉)〉
with 〈. . .〉 denoting the equilibrium averaging.
The generalized hydrodynamic fluxes Id
k,ι can be defined in the standard way:
ikId
k,ι = (1− PH)iLN P̂ ι
k
, (7)
where PH is the Mori-like projection operator, constructed on the set of all hydrodynamic variables
(5), and iLN is the Liouville operator. Thus, for the number density flux one can easily obtain
ikIdk,α =
ik
mα
(
ĴL
k,α −
mαcα
m̄
ĴL
k
)
, (8)
43602-2
Some rigorous relations for partial conductivities in ionic liquids
where mα is the particle mass in the α-th species, cα = Nα/N = nα/n denotes concentrations,
and m̄ =
∑
α
cαmα is the mean mass per particle.
The generalized (k, z)-dependent transport coefficients are defined via the generalized fluxes
Id
k,ι as follows [4, 5]
Lικ(k, z) =
β
V
∞
∫
0
dt exp{−zt}
(
Idk,ι, exp{−(1− PH)iLN t}Id−k,κ
)
. (9)
Note that the expression (9) has the structure of the well-known Green-Kubo formulas [6], but
the evolution operator is more complicated and additionally involves the projection operator PH.
However, in the hydrodynamic limit (k, z) → 0 one gets the expression
Lικ = lim
k,z→0
Lικ(k, z) =
β
V
∞
∫
0
dt
(
Idι , exp{−iLNt}Idκ
)
, (10)
that is commonplace in numerous textbooks (e.g. [7]) and has been routinely employed in computer
simulations.
In the context of this paper we are mainly interested in the behavior of the generalized mutual
diffusion coefficients Dαγ(k, z) that are simply related to the corresponding transport coefficients
Lαγ(k, z). Namely, one has
Lαγ(k, z) = ncαcγDαγ(k, z)/kBT, (11)
where n = N/V . The explicit frequency dependence in (9) can be found by taking into account
that z = iω + ε and ε → +0.
In general for a ν-component mixture the matrix of mutual diffusion coefficients D(k, ω) =
‖Dαγ(k, ω)‖ has ν × ν elements. Due to the symmetry properties Dαγ(k, ω) = Dγα(k, ω) this
number is reduced to the ν(ν + 1)/2 independent elements. However, there are still additional
ν explicit relations that follow from the total momentum conversation law. Namely, taking into
account that
ν
∑
α=1
mαI
d
k,α =
ν
∑
α=1
(
ĴL
k,α −
mαcα
m̄
ĴL
k
)
≡ 0 (12)
and using the definition (9), the set of new useful relations for generalized transport coefficients, that
involve the processes caused by number densities fluctuations, can be easily derived. In particular,
one gets
ν
∑
α=1
mαcαDαγ(k, ω) =
ν
∑
γ=1
Dαγ(k, ω)cγmγ ≡ 0. (13)
Hence, taking into account the relations (13) one can conclude that the total number of independent
matrix elements in the matrix D(k, ω) = ‖Dαγ(k, ω)‖ is equal to ν(ν − 1)/2. In a particular case
of binary mixture (ν = 2) we have ν(ν − 1)/2 = 1 and
D11(k, ω)
D12(k, ω)
= −
m2
m1
c2
c1
,
D11(k, ω)
D22(k, ω)
=
m2
2
m2
1
c22
c21
. (14)
These relations directly follow from the identity (13). Being valid for an arbitrary binary mixture,
they are of rather general character.
2. Binary mixture of charged particles
Let us now consider the case of a binary mixture composed of oppositely charged particles with
charges q+ and q−, massesm+ and m−, and densities n+, n−. The total electroneutrality condition
is satisfied, so that q+n+ + q−n− = 0.
43602-3
I. Mryglod, V. Kuporov
The electrical conductivity can be calculated by means of the Green-Kubo formula [8, 9]
σ =
β
V
∞
∫
0
dt〈Iq(t)Iq(0)〉, (15)
where Iq(t) =
∑
α
Iqα(t) with
Iqα(t) = qαnα
Nα
∑
i=1
vα
i
being the partial ionic electrical current (α = +,−). Ionic conductivity is also connected with the
mutual diffusion coefficients [9]:
σ =
n
kBT
∑
α,β
qαqβcαcβDαβ , (16)
where mutual diffusion coefficients are defined as follows
Dαβ =
N
NαNβ
Nα,Nβ
∑
i,j=1
∞
∫
0
dt
〈
vα
i (t)v
β
j (0)
〉
with α, β = +,−. In the center of mass reference frame the expression (16) can be easily derived
from (15) with the help of equations (8), (9) and (11). For generalized (k, ω)-dependent ionic
conductivity one can use the definition
σ(k, ω) =
n
kBT
∑
α,β
qαqβcαcβDαβ(k, ω). (17)
It is seen from (17) that the total ionic conductivity can be presented as the sum of partial
ionic conductivity σ = σ+ + σ−, where σα ∼ qαcα
∑
β qβcβDαβ , so that for the ratio of partial
ionic conductivity one gets
σ+
σ−
=
q2+c
2
+D++ + q+c+q−c−D+−
q2−c
2
−D−− + q+c+q−c−D+−
. (18)
This expression can be significantly simplified if we use the relations that follow from (14),
namely: D++/D−− = (m2
−/m
2
+)(c
2
−/c
2
+), D++/D+− = −(m−/m+)(c−/c+), D−−/D−+ =
−(m+/m−)(c+/c−), D+− = D−+. Taking into account the electroneutrality condition q+c+ +
q−c− = 0, one gets
σ+(k, ω)
σ−(k, ω)
= −
q+
q−
m−
m+
. (19)
In the case of charge-symmetric systems with q− = −q+ (in particular, for molten salts NaCl, KCl,
NaF, KF, RbBr) we obtain
σ+(k, ω)
σ−(k, ω)
=
m−
m+
. (20)
In fact, the expression (20) represents the generalized version of the so-called “universal golden
rule” (1) valid for binary charge-symmetric ionic liquids with arbitrary values (k, ω). In a more
general form (19) such a relation is derived for a charge-asymmetric binary mixture by means of
the rigorous expressions (13) obtained for the generalized mutual diffusion coefficients of a multi-
component fluid.
43602-4
Some rigorous relations for partial conductivities in ionic liquids
3. Ternary mixtures
3.1. Charged particles in solvent
Let us consider a more complicated model of a ternary mixture that is composed of oppositely
charged particles in neutral solvent with the particle charges q+ and q−, the particle masses m+,
m−, and m0, and concentrations c+, c−, c0 (c++c−+c0 = 1). The total electro-neutrality condition
can be written in the form: q+c+ + q−c− = 0.
From the relations (13) one obtains the equations
m+c+D++(k, ω) +m−c−D−+(k, ω) +m0c0D0+(k, ω) ≡ 0,
m+c+D+−(k, ω) +m−c−D−−(k, ω) +m0c0D0−(k, ω) ≡ 0,
m+c+D+0(k, ω) +m−c−D−0(k, ω) +m0c0D00(k, ω) ≡ 0, (21)
where Dαβ = Dβα. The electroneutrality condition enables us to express the concentrations of
charged particles via c0, namely: c+ = (1 − c0)q−/(q− − q+), c− = (1 − c0)q+/(q+ − q−). It is
obvious that
q2+c
2
+ = q2−c
2
− = (1 − c0)
2 q2+q
2
−
(q+ − q−)2
≡ Q2,
q+c+q−c− = −(1− c0)
2 q2+q
2
−
(q+ − q−)2
≡ −Q2.
Therefore, one gets σ+ = Q2(D++−D+−) and σ− = Q2(D−−−D+−), so that the expression (18)
for the ratio of partial ionic conductivities can be rewritten in the form
σ+(k, ω)
σ−(k, ω)
=
D++(k, ω)−D+−(k, ω)
D−−(k, ω)−D+−(k, ω)
. (22)
Combining the first two equations in (21), one can obtain:
m+c+(D++ −D+−)−m−c−(D−− −D+−) +m0c0(D0+ −D0−) ≡ 0 (23)
or
m+c+σ+ −m−c−σ− +m0c0∆ = 0, (24)
where the quantity ∆ ≡ Q2(D0+ −D0−) is expressed in terms of the mutual diffusion coefficients
for ions in solvent. The relation (24) could be considered as the generalization of “universal golden
rule” for solutions of electrolytes. Note that in the limit c0 → 0 the expression (22) can be easily
recovered from (22).
3.2. Pseudo-binary molten salts
A special class of ternary ionic liquids is formed by the so-called pseudo-binary molten salts,
for instance KCl−NaCl. In this case we deal with a ternary mixture of ions. In particular, for
KCl−NaCl in the system with the elementary charge e = 1 the ionic charges are qNa = qK = 1
and qCl = −1 with the electro-neutrality condition cNa + cK = cCl, where cNa + cK + cCl = 1.
For the mutual diffusion coefficients from (13) one has:
m1c1D11(k, ω) +m2c2D21(k, ω) +m3c3D31(k, ω) ≡ 0,
m1c1D12(k, ω) +m2c2D22(k, ω) +m3c3D32(k, ω) ≡ 0,
m1c1D13(k, ω) +m2c2D23(k, ω) +m3c3D33(k, ω) ≡ 0, (25)
where {K,Na,Cl} ↔ {1, 2, 3}.
Using the definition for partial ionic conductivities σα(k, ω),
σα(k, ω) = qαcα
∑
β
qβcβDαβ(k, ω), (26)
43602-5
I. Mryglod, V. Kuporov
we obtain the expressions:
σK(k, ω) ≡ σ1(k, ω) = c1 [c1D11(k, ω) + c2D12(k, ω)− c3D13(k, ω)],
σNa(k, ω) ≡ σ2(k, ω) = c2 [c1D21(k, ω) + c2D22(k, ω)− c3D23(k, ω)],
σCl(k, ω) ≡ σ3(k, ω) = −c3 [c1D31(k, ω) + c2D32(k, ω)− c3D33(k, ω)]. (27)
If we multiply each equation in (27) by m1, m2 and (-m3), respectively, add them and use the
identities (25), it is easy to obtain the following relation
m1σ1(k, ω) +m2σ2(k, ω) = m3σ3(k, ω), (28)
or
mKσK(k, ω) +mNaσNa(k, ω) = mClσCl(k, ω). (29)
In the hydrodynamic limit when (k, ω) → 0 this result was obtained in [3] by means of the Langevin
equation and confirmed directly by molecular dynamics simulations. We note that relation (29)is
valid for arbitrary (k, ω).
Using (28) one can write
mAσA(k, ω) +mBσB(k, ω) = mIσI(k, ω), (30)
for a pseudo-binary electrolyte AI− BI with ion charges qA = qB = −qI.
4. Multi-component mixture of charged particles
Let us now consider the model of a multi-component fluid composed of Nα ions with charges
qα in the αth species (α = 1, 2, . . . , ν). Mutual diffusion coefficients Dαβ(k, ω) of the system should
satisfy the relations (13). For partial ionic conductivities one has the definition (26), so that if we
multiply σα(k, ω) by mα/qα one can write
∑
α
mα
qα
σα(k, ω) =
∑
α
mαcα
∑
β
qβcβDαβ(k, ω)
=
∑
β
qβcβ
[
∑
α
mαcαDαβ(k, ω)
]
. (31)
Taking into account (13) we finally obtain
∑
α
mα
qα
σα(k, ω) ≡ 0. (32)
This is a rather general result that includes, as a particular case, the relation (30), derived above.
For example, using (32) it is easy to obtain the relation for partial ionic conductivities for pseudo-
binary four-component mixture AnIl − BkYj with different charges of ions.
A more complicated case corresponds to the model of a (ν+ν̄)-component fluid that is composed
of Nα ions with charges qα (α = 1, 2, . . . , ν) and Nᾱ neutral particles belonging to the ᾱth species
(ᾱ = 1, 2, . . . , ν̄). In this case the equation (31) should be rewritten in the form
ν
∑
α=1
mα
qα
σα(k, ω) =
ν
∑
β=1
qβcβ
[
ν
∑
α=1
mαcαDαβ(k, ω)
]
= −
ν
∑
β=1
qβcβ
[
ν̄
∑
ᾱ=1
mᾱcᾱDᾱβ(k, ω)
]
, (33)
where the relations (13) have been used. Note that the index ᾱ denotes the neutral particles.
Therefore, on the right hand side of (33) the effects of mutual diffusion of all the ions in solvent are
included. It is obvious that in particular case of a ternary mixture of charged particles in neutral
solvent, the expression (24) can be easily recovered from (33).
43602-6
Some rigorous relations for partial conductivities in ionic liquids
The expression (33) can be further simplified if we introduce two new densities, namely the
mass density of solvent M̂k (formed by neutral particles only) and the charge density Q̂k:
M̂k =
ν̄
∑
ᾱ=1
mᾱcᾱN̂k,ᾱ , Q̂k =
ν
∑
α=1
qαcαN̂k,α . (34)
Now we can rewrite (34) in the form
ν
∑
α=1
mα
qα
σα(k, ω) = −DMQ(k, ω), (35)
where the generalized transport coefficient
DMQ(k, ω) =
ν̄
∑
ᾱ=1
ν
∑
β=1
mᾱcᾱ Dᾱβ(k, ω) qβcβ
describes the diffusive ion-solvent cross-correlations. The relation (35) yields, in fact, the most
general form of identity valid for partial ionic conductivities of classical systems of charged particles
at arbitrary (k, ω).
5. Conclusions
It is shown that the general relations, that link partial ionic conductivities in a binary mixture
of charged particles, three- and four-component pseudo-binary molten salts as well as in multi-
component classical fluids of charged particles, can be derived by means of rigorous expressions,
obtained previously for the mutual diffusion coefficients of multi-component liquids. Some of these
relations generalize the results known in the literature (see, for instance, [2]), but most of them
are new. Moreover, all of these relations are valid for (k, ω)-dependent quantities and this, in
particular, explains the results of molecular dynamic simulations of the frequency-dependent partial
conductivities carried out [10] for molten NaCl and NaI.
References
1. Sundheim B.R., J. Phys. Chem., 1956, 60, 1381.
2. Koishi T., Kawase S., Tamaki S., J. Chem. Phys., 2002, 116, 3018; Koishi T., Tamaki S., J. Chem.
Phys., 2004, 121, 333.
3. Matsunaga S., Koishi T., Tamaki S., Proc. of the AIP Conference, 2008, 982, 399.
4. Mryglod I., Condens. Matter Phys., 1997, 10, 115.
5. Mryglod I., Bryk T., Kuporov V., Collective dynamics in ionic liquids: A comparative study with non-
Coulombic fluids. – In: NATO Science Series II, Eds. D. Henderson, M. Holovko, A. Trokhymchuk, Vol.
206, 2005, p. 109.
6. Kubo R.J., Phys. Soc. Jpn., 1957, 12, 570.
7. Zubarev D.N., Morozov V.G., Röpke G., Statistical mechanics of nonequilibrium processes, Vol. 2:
Relazation and hydrodynamic processes. Akademie Verlag, Berlin, 1997.
8. Hansen J.P., McDonald I.R., Phys. Rev. A, 1975, 11, 2111.
9. Trullas J., Padro J.A., J. Chem. Phys., 1993, 99(5), 3983.
10. Koishi T., Tamaki S., J. Phys. Soc. Jpn., 1999, 68, 964.
43602-7
I. Mryglod, V. Kuporov
Деякi строгi спiввiдношення для парцiальних провiдностей в
iонних рiдинах
I. Мриглод1,2, В. Купоров2
1 Iнститут фiзики конденсованих систем НАН України, 79011 Львiв, вул. Свєнцiцького, 1
2 Iнститут прикладної математики i фундаментальних наук Нацiонального унiверситету “Львiвська
полiтехнiка”, 79013 Львiв, Україна
Стартуючи з точних спiввiдношень, що були виведенi нами нещодавно для узагальнених коефiцiєнтiв
переносу в багатокомпонентних плинах, ми отримали кiлька строгих спiввiдношень для парцiальних
провiдностей в iонних зарядово-асиметричних сумiшах. Для найпростiшого випадку зарядово-
симетричної бiнарної системи таке спiввiдношення було виявлене експериментально Сундхеймом
бiльш нiж 50 рокiв тому i вiдоме як “унiверсальне золоте правило”. Розглянуто також деякi
бiльш складнi моделi, що описують, зокрема, випадки потрiйних та багатокомпонентних сумiшей.
Виведено загальне спiввiдношення для парцiальних iонних провiдностей багатокомпонентного
iонного плину. Показано, що такого типу спiввiдношення є фактично лише одним з прикладiв бiльш
широкого класу виразiв, що дiйснi для (k, ω)-залежних величин.
Ключовi слова: iоннi рiдини, коефiцiєнти переносу, коефiцiєнти взаємної дифузiї, iонна
провiднiсть, розплави солей
43602-8
Theoretical framework
Binary mixture of charged particles
Ternary mixtures
Charged particles in solvent
Pseudo-binary molten salts
Multi-component mixture of charged particles
Conclusions
|
| id | nasplib_isofts_kiev_ua-123456789-32129 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-07T17:15:02Z |
| publishDate | 2010 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Mryglod, I. Kuporov, V. 2012-04-09T21:22:06Z 2012-04-09T21:22:06Z 2010 Some rigorous relations for partial conductivities in ionic liquids / I. Mryglod, V. Kuporov // Condensed Matter Physics. — 2010. — Т. 13, № 4. — С. 43602:1-8. — Бібліогр.: 10 назв. — англ. 1607-324X PACS: 66.10.cg, 66.10.Ed, 82.45.Gj, 47.10.-g https://nasplib.isofts.kiev.ua/handle/123456789/32129 Starting with the rigorous expressions, derived previously for the generalized transport coefficients of a multicomponent fluid, we obtained several exact relations for partial conductivities of ionic charge-asymmetric mixtures. For a simpler case of a charge-symmetric binary mixture such kind of relations was discovered experimentally by Sundheim more than 50 years ago and is known as the “universal golden rule”. Some more complicate models, describing in particular the cases of ternary and multi-component mixtures, are considered. The general relation for partial ionic conductivities is derived for a multi-component ionic fluid. It is shown that such relations can be considered in fact as an example of a more general class of rigorous expressions valid for (k, ω)-dependent quantities. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Some rigorous relations for partial conductivities in ionic liquids Деякі строгі співвідношення для парціальних провідностей в іонних рідинах Article published earlier |
| spellingShingle | Some rigorous relations for partial conductivities in ionic liquids Mryglod, I. Kuporov, V. |
| title | Some rigorous relations for partial conductivities in ionic liquids |
| title_alt | Деякі строгі співвідношення для парціальних провідностей в іонних рідинах |
| title_full | Some rigorous relations for partial conductivities in ionic liquids |
| title_fullStr | Some rigorous relations for partial conductivities in ionic liquids |
| title_full_unstemmed | Some rigorous relations for partial conductivities in ionic liquids |
| title_short | Some rigorous relations for partial conductivities in ionic liquids |
| title_sort | some rigorous relations for partial conductivities in ionic liquids |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/32129 |
| work_keys_str_mv | AT mryglodi somerigorousrelationsforpartialconductivitiesinionicliquids AT kuporovv somerigorousrelationsforpartialconductivitiesinionicliquids AT mryglodi deâkístrogíspívvídnošennâdlâparcíalʹnihprovídnosteivíonnihrídinah AT kuporovv deâkístrogíspívvídnošennâdlâparcíalʹnihprovídnosteivíonnihrídinah |