A Gibbs energy minimization method for constrained and partial equilibria

Research output: Contribution to journalArticleScientificpeer-review

21 Citations (Scopus)

Abstract

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
Volume83
Issue number6
DOIs
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

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Gibbs free energy
Conservation
Lagrange multipliers
Chemical potential
Free energy
Suspensions
Fibers

Keywords

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

Cite this

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title = "A Gibbs energy minimization method for constrained and partial equilibria",
abstract = "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.",
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A Gibbs energy minimization method for constrained and partial equilibria. / Koukkari, Pertti; Pajarre, Risto.

In: Pure and Applied Chemistry, Vol. 83, No. 6, 2011, p. 1243-1254.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - A Gibbs energy minimization method for constrained and partial equilibria

AU - Koukkari, Pertti

AU - Pajarre, Risto

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Donnan equilibrium

KW - extent of reaction

KW - Gibbs energy

KW - immaterial constraints

KW - minimization

KW - surface energy

KW - virtual components

U2 - 10.1351/PAC-CON-10-09-36

DO - 10.1351/PAC-CON-10-09-36

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VL - 83

SP - 1243

EP - 1254

JO - Pure and Applied Chemistry

JF - Pure and Applied Chemistry

SN - 0033-4545

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ER -