calc_assoc_matrices

despasito.equations_of_state.saft.Aassoc.calc_assoc_matrices

calc_assoc_matrices(beads, bead_library, molecular_composition, cross_library={}, nk=None, sitenames=None)[source]

Generate matrices used for association site calculations.

Compute epsilonHB (interaction energy for association term), Kklab (association interaction bonding volume, and nk (number of sites )

Note: Some papers use rc_klab instead of Kklab. In those cases, a function to calculate Kklab is needed (see Papaioannou 2014).

Parameters:

  • beads (list[str]) – List of unique bead names used among components

  • bead_library (dict) – A dictionary where bead names are the keys to access EOS self interaction parameters:

    • epsilonHB-*-*: Optional, Interaction energy between each bead and

    association site. Asterisk represents string from sitenames. - K-*-*: Optional, Bonding volume between each association site. Asterisk represents two strings from sitenames. - rc-*-*: Optional, Cutoff distance for association sites. Asterisk represents two strings from sitenames. - rd-*-*: Optional, Site position. Asterisk represents two strings from sitenames. - Nk-*: Optional, The number of sites of from list sitenames. Asterisk represents string from sitenames.

  • molecular_composition (numpy.ndarray) – \(\nu_{i,k}/k_B\). Array of number of components by number of bead types. Defines the number of each type of group in each component.

  • cross_library (dict, Optional, default={}) – A dictionary where bead names are the keys to access a dictionary of a second tier of bead names. This structure contains the EOS cross interaction parameters:

    • epsilonHB-*-*: Optional, Interaction energy between each bead and

    association site. Asterisk represents string from sitenames. - K-*-*: Optional, Bonding volume between each association site. Asterisk represents two strings from sitenames. - rc-*-*: Optional, Cutoff distance for association sites. Asterisk represents two strings from sitenames. - rd-*-*: Optional, Site position. Asterisk represents two strings from sitenames.

  • nk (numpy.ndarray, Optional, default=None) – A matrix of (Nbeads x Nsites) Contains for each bead the number of each type of site

  • }

  • sitenames (list, Optional, default=None) – This list shows the names of the various association types found

Returns:

output_dict – This dictionary contains parameters relevant to calculating association site contributions. The following matrices may be inside, each of the size (ngroups, ngroups, nsites, nsites).

  • epsilonHB: Interaction energy between each bead and association site.

  • Kklab, Optional: Bonding volume between each association site

  • rc_klab, Optional: Cutoff distance for association sites

  • rd_klab, Optional: Association site position

Return type:

dict