electrolyte-ion-content
Definition of electrolyte: An aqueous solution containing dissolved
ions that result from the dissociation of salts.
The pH value of this solution is related to the concentration of H3O+
and OH- ions.
There are two ways how the electrolyte influences the calculations:
- oxide/electrolyte interface states:
$interface-states
- Poisson-Boltzmann equation in electrolyte region:
$electrolyte
$electrolyte-ion-content
The electrostatic potential distribution in the electrolyte can be finally
obtained by solving the nonlinear Poisson-Boltzmann equation with appropriate
boundary conditions.
The Poisson-Boltzmann model describes the equilibrium of
electro-diffusion processes of ions in a solution. There is an exponential
relationship between the distribution of the charge density and the potential.
Note: The material name of the electrolyte region must be identical to
'Electrolyte':
$material
material_name = Electrolyte
If the electrolyte is present at grid point i, then call
SUBROUTINE calculate_class_dens_ion to calculate the ion density
(Poisson-Boltzmann equation).
- FUNCTION
density
- FUNCTION
deriv_density
Electrolyte:
1D:
Note: The electrolyte region should be placed at the boundary of the
one-dimensional device, i.e. the device should basically look like this along z-direction:
metal (=contact) -
semiconductor heterostructure - oxide - electrolyte - metal (contact=electrode inside the
electrolyte)
2D:
Then solve the current in the device for direction perpendicular to z direction, i.e. along x
and y:
metal (=contact) - semiconductor heterostructure - (here flows the current, so
we need two additional contacts in a 2D simulation) - oxide - electrolyte -
metal (contact=electrode inside the
electrolyte)
!----------------------------------------------------!
$electrolyte-ion-content
optional !
ion-number
integer
required !
ion-name
character
optional !
ion-valency
double
required !
ion-concentration
double
required !
ion-region
double_array required !
$end_electrolyte-ion-content
optional !
!----------------------------------------------------!
Syntax
ion-number =
1
= 2
Numbering must be unique. All ion numbers numbers together must form a dense set
1, 2, 3, ..., maxnumber.
ion-name =
Na+ !
cation+ of NaCl
= Cl- !
anion- of NaCl
= Ca2+ !
cation2+ of CaCl2
= Cl- !
anion- of CaCl2
(optional)
ion-valency =
1d0
= -2d0
should be an integer, e.g. ...,-2,-1,0,1,2,...
This is the charge of the ion.
(Can be set zero if one wants to deactivate it.)
ion-concentration = 1.0d-3 ! [M]=[mol/l]
ion concentration of this ion-number in the electrolyte in units
of [M] = [mole/liter] = 1d-3 [mol/cm³]
ion-region =
100d0 2000d0 ! [nm]
refers to region where the electrolyte has to be applied to, e.g.
from 100 nm to 2000 nm in 1D (xmin xmax)
- 1D simulation: xmin xmax
- 2D simulation: xmin xmax ymin ymax
- 3D simulation: xmin xmax ymin ymax zmin zmax
1D Example:
!---------------------------------------------------------------------------!
! The electrolyte (NaCl, Hepes) contains four types of ions:
! 1) 100 mM singly charged cations (Na^+)
! 2) 100 mM singly charged anions (Cl^-)
! 3) 10 mM doubly charged cations (Hepes solution ^2+)
! 4) 20 mM singly charged anions (Hepes solution ^-)
!---------------------------------------------------------------------------!
$electrolyte-ion-content
ion-number =
1
ion-name =
Na+ !
Na+
ion-valency =
1d0 !
charge of the ion: Na+
ion-concentration = 0.100d0
! Input in units of: [M] = [mol/l] = 1d-3 [mol/cm³]
ion-region =
1543d0 9999d0 ! refers to region where
the electrolyte has to be applied to
ion-number =
2
ion-name =
Cl- !
Cl-
ion-valency =
-1d0 ! Cl-
ion-concentration = 0.100d0
! Input in units of: [M] = [mol/l] = 1d-3 [mol/cm³]
ion-region =
1543d0 9999d0 ! refers to region where
the electrolyte has to be applied to
ion-number =
3 !
ion-name =
Hepes2+ ! Hepes2+
ion-valency =
2d0 ! Hepes2+
ion-concentration = 0.010d0
! Input in units of: [M] = [mol/l] = 1d-3 [mol/cm³]
ion-region =
1543d0 9999d0 ! refers to region where
the electrolyte has to be applied to
ion-number =
4 !
ion-name =
Hepes- ! Hepes-
ion-valency =
-1d0 ! Hepes-
ion-concentration = 0.020d0
! Input in units of: [M] = [mol/l] = 1d-3 [mol/cm³]
ion-region =
1543d0 9999d0 ! refers to region where
the electrolyte has to be applied to
$end_electrolyte-ion-content
!---------------------------------------------------------------------------!
Buffer solutions
Note: Instead of specifying the buffer ions explicitly under keyword
$electrolyte-ion-content it is much more
convenient (and userfriendly) to use the specifer buffer-name =
HEPES (or any other buffer name) in keyword
$electrolyte.
By doing so, the concentration of the various buffer ions is calculated
automatically, taking into account the pH value, the pKa
value, the number of relevant ions, the ionic strength and the temperature
dependence in a self-consistent manner.
The material parameters for the various buffer solutions can be found in the
database under this keyword:
$buffer-solutions.
Limitations:
- Currently the ion-region must extend over the whole electrolyte region.
- Only one electrolyte region is possible
- Even if no ions are present in the electrolyte (apart from H3O+, OH-,
anion-, cation+), at least one ion species
has to be specified. But you can specify ion-concentration = 0d0
in this case.
- Note that the overall charge in the electrolyte should be zero, i.e. the
electrolyte should be neutral (electroneutrality requirement).
Bascially, the salts that are put into the electrolyte are neutral. So
the sum over all dissociated ions of the salts should also be neutral.
It could be that the user forgets some of these dissociated ions,
specifies the valency incorrectly or specifies the concentration incorrectly.
Luckily, these cases will be checked inside the code.
pH value
Note: The ion concentrations of H3O+ and OH-
(and their corresponding anion- and cation+ counterparts) must not be
specified here.
- corresponding anion-: conjugate base (Example: HCl + H2O
<==> H3O+ + Cl- :
Cl- is the conjugate base)
- corresponding cation+: conjugate acid
They are inserted automatically inside the code.
nextnano³ automatically generates the following entries internally for
the specified pH values:
(i is the total number of ions
specified in the input file)
pH = 7 (neutral) ([H3O+]
= [OH-] = 1 * 10-7
M):
ion-number =
(i+1) !
H3O+
ion-name =
H3O+ !
ion-valency = 1d0
! ^1+
ion-concentration = 1.0d-7
! Input in units of: [M] = [mol/l] = 1d-3 [mol/cm³]
ion-region =
(same as 1st ion) ! refers to region where
the electrolyte has to be applied to
ion-number =
(i+2) ! -
ion-name =
OH- ! -
ion-valency =
-1d0 ! -: ^1-
ion-concentration = 1.0d-7 ! Input
in units of: [M] = [mol/l] = 1d-3 [mol/cm³]
ion-region =
(same as 1st ion) ! refers to region where
the electrolyte has to be applied to
ion-number =
(i+3) ! - (corresponding to H3O+)
ion-name =
anion- ! - (corresponding to H3O+)
ion-valency =
-1d0 ! -: ^1-
ion-concentration = 0d0 !
No conjugate base present for pH = 7 (neutral, i.e. pure water)
ion-region =
(same as 1st ion) !
ion-number =
(i+4) ! (corresponding to OH-)
ion-name =
cation+ ! (corresponding to OH-)
ion-valency =
+1d0 ! ^1+
ion-concentration = 0d0 !
No conjugate acid present for pH = 7 (neutral, i.e. pure water)
ion-region =
(same as 1st ion) !
pH = 0 (acid) ([H3O+]
= 1 M; [OH-] =
1 * 10-14 M):
ion-number =
(i+1) !
H3O+
ion-valency = 1d0
! ^1+
ion-concentration = 1.0d0
! Input in units of: [M] = [mol/l] = 1d-3 [mol/cm³]
...
ion-number =
(i+2) !
OH-
ion-valency =
-1d0 ! -: ^1-
ion-concentration = 1.0d-14 ! Input
in units of: [M] = [mol/l] = 1d-3 [mol/cm³]
...
ion-number =
(i+3) !
anion- (corresponding to H3O+)
ion-valency =
-1d0 ! -: ^1-
ion-concentration = ~1d0 !
= 10-pH - 10-pOH = 10-0 - 10-14 = 1
...
ion-number =
(i+4) ! (corresponding to OH-)
ion-valency =
+1d0 ! ^1+
ion-concentration = 0d0 !
No conjugate acid present for pH < 7 (i.e. acid)
...
pH = 14 (base) ([H3O+]
= 1 * 10-14 M; [OH-]
= 1 M):
ion-number =
(i+1) !
H3O+
ion-valency = 1d0
! ^1+
ion-concentration = 1.0d-14
! Input in units of: [M] = [mol/l] = 1d-3 [mol/cm³]
...
ion-number =
(i+2) !
OH-
ion-valency =
-1d0 ! -: ^1-
ion-concentration = 1.0d0 ! Input
in units of: [M] = [mol/l] = 1d-3 [mol/cm³]
...
ion-number =
(i+3) !
anion- (corresponding to H3O+)
ion-valency =
-1d0 ! -: ^1-
ion-concentration = 0d0 !
No conjugate base present for pH > 7 (i.e. base)
...
ion-number =
(i+4) ! (corresponding to OH-)
ion-valency =
+1d0 ! ^1+
ion-concentration = ~1d0 !
= 10-pOH - 10-pH = 10-0 - 10-14 = 1
...
The pH value has to be specified in keyword
$interface-states by the specifier
pH-value for the state-type = electrolyte.
Extremal pH values
At extremal pH values, the following ions are present:
pH = 0: 1 mol/l H3O+, ~1 mol/l anion-
(conjugate base)
(negligible: 1*10-14 mol/l
OH-; 0 mol/l cation+)
pH = 14: 1 mol/l OH-, ~1 mol/l cation+ (conjugate
acid)
(negligible: 1*10-14 mol/l H3O+;
0 mol/l anion-)
This means that these ions will dominate over all other specified ion species
unless they occur in a comparable concentration.
If the density of surface sites is zero ($interface-states, state-type =
electrolyte, interface-density =
0d0) and if no other ions are
specified then the results for very extreme pH values should be
identical:
Result(
pH=0 ) = Result( pH=14 ) => Strong acid and strong base
should lead to identical results
because nextnano³ does not distinguish between H3O+
and cation+. It also does not distinguish between OH-
and anion-.
More information on electrolyte:
$electrolyte
More information on electrolyte interface charges (site-binding model):
$interface-states
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