A Gibbs energy minimization method for constrained and partial equilibria

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The conventional Gibbs energy minimization methods apply elemental amounts of system components as conservation constraints in the form of a stoichiometric conservation matrix. The linear constraints designate the limitations set on the components described by the system constituents. The equilibrium chemical potentials of the constituents are obtained as a linear combination of the component-specific contributions, which are solved with the Lagrange method of undetermined multipliers. When the Gibbs energy of a multiphase system is also affected by conditions due to immaterial properties, the constraints must be adjusted by the respective entities. The constrained free energy (CFE) minimization method includes such conditions and incorporates every immaterial constraint accompanied with its conjugate potential. The respective work or affinity-related condition is introduced to the Gibbs energy calculation as an additional Lagrange multiplier. Thus, the minimization procedure can include systemic or external potential variables with their conjugate coefficients as well as non-equilibrium affinities. Their implementation extends the scope of Gibbs energy calculations to a number of new fields, including surface and interface systems, multi-phase fiber suspensions with Donnan partitioning, kinetically controlled partial equilibria, and pathway analysis of reaction networks.
Original languageEnglish
Pages (from-to)1243-1254
Number of pages12
JournalPure and Applied Chemistry
Issue number6
Publication statusPublished - 2011
MoE publication typeA1 Journal article-refereed
Event21st International Conference on Chemical Thermodynamics (ICCT-2010) - Tsukuba, Japan
Duration: 1 Aug 20106 Aug 2010


  • Donnan equilibrium
  • extent of reaction
  • Gibbs energy
  • immaterial constraints
  • minimization
  • surface energy
  • virtual components

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