Model Chi Multi-Species Charge

Arguments:

  • type (string) - Name of the model to use (ChiMultiSpeciesCharge)

  • Nref (float) - Reference degree of polymerization

  • bref (float) - Reference statistical segment length

  • initfields (json object) - Describes how to initialize fields within model. See Initialize Model Fields

  • C or rho0 (float) - System density \(C = \rho_0 R_g^3 / N_{ref}\). Only one can be specified. Default: C=1.

  • inverse_zetaN or zeta (float) - Helfand compressibility parameter \(\zeta\), optionally multiplied by Nref and inverted (i.e. \((\zeta N)^{-1}\)). Cannot be specified if inverse_BC or B or u0 are specified. Default: inverse_zetaN = 0 (incompressible)

  • inverse_BC or B or u0 (float) - Excluded volume incompressiblity. \(B =\beta u_0 N^2 / R_g^3\) is the dimensionless excluded volume and \(C = n R_g^3 / V\). Cannot be specified if inverse_zetaN or zeta are specified.

Note

Only one compressibility parameter (i.e. u0, B, zeta, inverse_zetaN or inverse_BC) can be specified.

  • chiN_array or chi_array (float array) - Flory-Huggins \(\chi\) parameters, optionally multiplied Nref. Ordering of array elements are \({\chi_1, \chi_2, \chi_3, ...}\) and correspond to the upper diagonal of the \(\pmb{\chi}\) interaction matrix.

  • chiN_diagonal or chi_diagonal (float array) - Flory-Huggins \(\chi^s_{ii}\) self interaction parameters, optionally multiplied Nref. This can be used to make some species more or less compressible than others. Length of array should be equal to number of species and corresponds to the diagonal elements of the \(\pmb{\chi}\) interaction matrix. Ordering of elements are \({\chi^s_{11}, \chi^{s}_{22}, \chi^s_{33}, ...}\)

  • E or lB (float) - Electrostatic interaction strength. Only one can be specified.

For a 3 species model:

\[\begin{split}\pmb{\chi} = \begin{pmatrix} \chi^s_{11} & \chi_1 & \chi_2 \\ \chi_1 & \chi^s_{22} & \chi_3 \\ \chi_2 & \chi_3 & \chi^s_{33} \\ \end{pmatrix}\end{split}\]

For a 4 species model:

\[\begin{split}\pmb{\chi} = \begin{pmatrix} \chi^s_{11} & \chi_1 & \chi_2 & \chi_3 \\ \chi_1 & \chi^s_{22} & \chi_4 & \chi_5 \\ \chi_2 & \chi_4 & \chi^s_{33} & \chi_6 \\ \chi_3 & \chi_5 & \chi_6 & \chi^s_{44} \\ \end{pmatrix}\end{split}\]

Example (python)

chiN = 30.0
fts.model(Nref=1.0,bref=1.0,inverse_zetaN=0.01,chiN_array=[chiN, chiN, chiN],E=1000, type='ChiMultiSpeciesCharge')

...

# to initialize EXCHANGE fields
fts.init_model_field(type='random',mean=0.0,stdev=1.0,fieldname='mu_1')
fts.init_model_field(type='random',mean=0.0,stdev=1.0,fieldname='mu_2')
fts.init_model_field(type='random',mean=0.0,stdev=1.0,fieldname='mu_3')

# to initialize SPECIES fields
fts.init_model_field(type='random',mean=0.0,stdev=1.0,fieldname='mu_A')
fts.init_model_field(type='random',mean=0.0,stdev=1.0,fieldname='mu_B')
fts.init_model_field(type='random',mean=0.0,stdev=1.0,fieldname='mu_C')

...

# three species must be present
fts.add_species(label='A',stat_segment_length=1.0, charge=+1)
fts.add_species(label='B',stat_segment_length=1.0, charge=0)
fts.add_species(label='C',stat_segment_length=1.0, charge=-1)

Example (json)

"model": {
  "type": "ChiMultiSpeciesCharge"
  "Nref": 1.0,
  "bref": 1.0,
  "E":1000,
  "chiN_array": [20,40,20] ,
  "initfields": {
    ... see "Initialize Model Fields" ...
  },
},

Model Chi Multi-Species Charge Formalism

Reference: Lequieu2024 https://pubs.acs.org/doi/10.1021/acs.macromol.4c02034