Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 1243-1254 |
| Number of pages | 12 |
| Journal | Pure and Applied Chemistry |
| Volume | 83 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2011 |
| MoE publication type | A1 Journal article-refereed |
| Event | 21st International Conference on Chemical Thermodynamics (ICCT-2010) - Tsukuba, Japan Duration: 1 Aug 2010 → 6 Aug 2010 |
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Keywords
- Donnan equilibrium
- extent of reaction
- Gibbs energy
- immaterial constraints
- minimization
- surface energy
- virtual components
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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 journal › Article › Scientific › peer-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
M3 - Article
VL - 83
SP - 1243
EP - 1254
JO - Pure and Applied Chemistry
JF - Pure and Applied Chemistry
SN - 0033-4545
IS - 6
ER -