## FCSys.Species.'H+'.Ionomer

H+ in ionomer

### Information

Extends from Modelica.Icons.Package (Icon for standard packages).

### Package Content

Name | Description
--- | ---
Fixed | Fixed properties

## FCSys.Species.'H+'.Ionomer.Fixed

Fixed properties

### Information

Assumptions:

1. The generalized resistivities (η, θ) are fixed (e.g., independent of thermodynamic state).
2. The electrochemical reaction rate is governed by the electrons. Therefore, the specific exchange current is zero (τ′ = 0) for protons.
3. The conductivity is mapped to the mobility of the protons by assuming that the mobility of the substrate (e.g., C19HF37O5S-) is zero.

The default electrical conductivity (σ = `8.3*U.S/U.m`) is for DuPontTM Nafion® N-112 [DuPontN112]. This is for the interaction between H+ and the solid; it does not include the additional voltage loss due to electro-osmotic drag (with H2O).

The default thermal resistivity (θ = `U.m*U.K/(0.1661*U.W)`) is of H gas (rather than H+) at 300 K from [Schetz1996, p. 139]. Table 1 lists the properties at other temperatures.

Table 1: Properties of H gas (not H+) [Schetz1996, p. 139]
T `/U.K` | η`*U.Pa*U.s` | θ`*U.W /(U.m*U.K)`
--- | --- | ---
200 | 1/3.8e-6 | 1/0.1197
300 | 1/5.3e-6 | 1/0.1661
400 | 1/6.7e-6 | 1/0.2094
500 | 1/8.1e-6 | 1/0.2507
600 | 1/9.3e-6 | 1/0.2906
700 | 1/10.6e-6 | 1/0.3292
800 | 1/11.8e-6 | 1/0.3670
900 | 1/13.0e-6 | 1/0.4040
1000 | 1/14.2e-6 | 1/0.4403
1100 | 1/15.3e-6 | 1/0.4761
1200 | 1/16.5e-6 | 1/0.5114
1300 | 1/17.6e-6 | 1/0.5462
1400 | 1/18.7e-6 | 1/0.5807
1500 | 1/19.8e-6 | 1/0.6149
1600 | 1/20.9e-6 | 1/0.6487
1700 | 1/22.0e-6 | 1/0.6823
1800 | 1/23.1e-6 | 1/0.7156
1900 | 1/24.2e-6 | 1/0.7488
2000 | 1/25.2e-6 | 1/0.7817
2100 | 1/26.3e-6 | 1/0.8144
2200 | 1/27.3e-6 | 1/0.8470
2300 | 1/28.4e-6 | 1/0.8794
2400 | 1/29.4e-6 | 1/0.9117
2500 | 1/30.5e-6 | 1/0.9438
2600 | 1/31.5e-6 | 1/0.9758
2700 | 1/32.5e-6 | 1/1.0077
2800 | 1/33.6e-6 | 1/1.0395
2900 | 1/34.6e-6 | 1/1.0711
3000 | 1/35.6e-6 | 1/1.1027
3100 | 1/36.6e-6 | 1/1.1347
3200 | 1/37.7e-6 | 1/1.1664
3300 | 1/38.7e-6 | 1/1.1978
3400 | 1/39.7e-6 | 1/1.2288
3500 | 1/40.7e-6 | 1/1.2592
3600 | 1/41.6e-6 | 1/1.2884
3700 | 1/42.5e-6 | 1/1.3171
3800 | 1/43.4e-6 | 1/1.3455
3900 | 1/44.4e-6 | 1/1.3735
4000 | 1/45.2e-6 | 1/1.4012
4100 | 1/46.1e-6 | 1/1.4290
4200 | 1/47.0e-6 | 1/1.4566
4300 | 1/47.9e-6 | 1/1.4842
4400 | 1/48.8e-6 | 1/1.5116
4500 | 1/49.7e-6 | 1/1.5389
4600 | 1/50.6e-6 | 1/1.5661
4700 | 1/51.5e-6 | 1/1.5933
4800 | 1/52.3e-6 | 1/1.6204
4900 | 1/53.2e-6 | 1/1.6477
5000 | 1/54.1e-6 | 1/1.6750

For more information, please see the Species model.

Extends from Ion (Base model for an ion).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Integer | n_inter | 0 | Number of exchange connections with other phases
Material properties
replaceable package Data | Characteristics.'H+'.Ionomer | Characteristic data
TimeAbsolute | nu | 1 | Thermal independity [T]
DiffusivityMassSpecific | zeta | 0 | ** [L2.M/(N.T)]
Fluidity | eta | Data.eta(T, v) | Fluidity [L.T/M]
ConductivityElectrical | sigma | 8.3*U.S/U.m | Electrical conductivity [N2.T/(L3.M)]
Independence factors
NumberAbsolute | k_intra_Phi[n_intra, n_trans] | ones(n_intra, n_trans) | For translational exchange among species within the phase [1]
NumberAbsolute | k_intra_Q[n_intra] | ones(n_intra) | For thermal exchange among species within the phase [1]
Initialization
Velocity | phi.start[n_trans] | 0 | Velocity [L/T]
Current | I.start[n_trans] | 0 | Current [N/T]
Velocity | phi_boundaries.start[n_trans, Side] | 0 | Normal velocities at the boundaries [L/T]
Force | f.start[n_trans] | 0 | Total normal translational force on pairs of boundaries [L.M/T2]
Force | minusDeltaf.start[n_trans] | 0 | Dynamic and nonequilibrium compression forces [L.M/T2]
Geometry
Length | kL[:] | L[cartTrans] | Effective transport length [L]
Initialization
Init | initMaterial | Init.none | Method of initializing the material state
Init | initEnergy | Init.temperature | Method of initializing the thermal state
Assumptions
Integer | n_trans | 1 | Number of transport axes
Integer | n_chem | 1 | Number of reaction and phase change processes
Formulation of the conservation equations
ConsThermo | consMaterial | ConsThermo.dynamic | Material
ConsTrans | consTransX | ConsTrans.steady | X-axis translational momentum
ConsTrans | consTransY | ConsTrans.steady | Y-axis translational momentum
ConsTrans | consTransZ | ConsTrans.steady | Z-axis translational momentum
ConsThermo | consEnergy | ConsThermo.steady | Energy
Axes with upstream discretization
Boolean | upstreamX | false | X
Boolean | upstreamY | false | Y
Boolean | upstreamZ | false | Z
Flow conditions
Boolean | approxVelocity | true | Calculate normal boundary velocities assuming uniform density

### Connectors

Type | Name | Description
--- | --- | ---
Intra | intra[n_intra] | Connectors to exchange translational momentum and energy within the phase
Inter | inter[n_inter] | Connectors to exchange translational momentum and energy with all other species
Dalton | dalton | Connector for additivity of pressure
Boundary | boundaries[n_trans, Side] | Connectors for transport
Chemical | chemical[n_chem] | Connector for reactions and phase change
Material properties
replaceable package Data | Characteristic data

### Modelica definition

    model Fixed "Fixed properties"
      extends Ion(
        redeclare replaceable package Data = Characteristics.'H+'.Ionomer,
        final Nu_Phi,
        final Nu_Q,
        final consRot,
        final upstreamX=false,
        final upstreamY=false,
        final upstreamZ=false,
        final initMaterial=Init.none,
        final consEnergy=ConsThermo.steady,
        consTransX=ConsTrans.steady,
        consTransY=ConsTrans.steady,
        consTransZ=ConsTrans.steady,
        final zeta=0,
        final N_IC,
        redeclare parameter Q.ResistivityThermal theta=U.m*U.K/(0.1661*U.W),
        final p_IC,
        final h_IC,
        final V_IC,
        final rho_IC,
        final g_IC,
        final T_IC,
        final nu=1,
        final tauprime,
        final N0,
        n_chem=1,
        sigma=8.3*U.S/U.m);

      // See the documentation for a table of values.

    end Fixed;