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 DuPont^TM 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;