Difference between revisions of "MSE Density Parameter Update"
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[[File:Density Term 2.jpg]] (Combinatorial term omitted) | [[File:Density Term 2.jpg]] (Combinatorial term omitted) | ||
− | where [[File: | + | where [[File:Term Term.jpg]] is a different interaction parameter from that of [[File:Term 4.1.jpg]] in the [[File:Term 5.jpg]] model. |
+ | The symmetrically normalized [[File:T7.jpg]](subscript UNIQ is omitted in the following text) needs to be converted to the unsymmetrically normalized value ([[File:T8.jpg]]) for density calculations in MSE. | ||
+ | '''Conversion from'''[[File:T7.jpg]]'''to''' [[File:T8.jpg]]: | ||
+ | Standard state chemical potentials in the two normalizations are related by | ||
+ | [[File:T9.jpg]] (or [[File:T10.jpg]]) | ||
+ | which is derived from equality of chemical potentials in two normalizations, and using [[File:T11.jpg]]1 in the infinite dilution limit. Derivatives of ’s with respect to pressure give volumes, i.e. | ||
+ | [[File:T12.jpg]] -> [[File:T13.jpg]] | ||
+ | Here is how to calculate [[File:T14.jpg]] | ||
+ | Analogous to [[File:T15.jpg]], [[File:T16.jpg]] can be defined as [[File:T17.jpg]] and derived from Eq. (1) as: | ||
+ | [[File:T18.jpg]] (2a) | ||
+ | |||
+ | At infinite dilution, | ||
+ | [[File:T19.jpg]] (2b) | ||
+ | |||
+ | Now,[[File:T20.jpg]] can be calculated from Eq. (3) by combining Eq (1) and (2b): | ||
+ | |||
+ | [[File:T21.jpg]] (3) | ||
+ | |||
+ | In Eq. (1) and (2), | ||
+ | |||
+ | |||
+ | [[File:T22.jpg]] [[File:T23.jpg]] (Correspond to D0JI, D1JI, D2JI) | ||
+ | Equation (3) is equivalent to the equation: | ||
+ | |||
+ | [[File:T24.jpg]], with [[File:T25.jpg]] | ||
+ | |||
+ | Solution volume is then calculated by | ||
+ | |||
+ | [[File:T26.jpg]] | ||
+ | |||
+ | Here [[File:T8.jpg]] is calculated from contributions of UNIQUAC and “middle-range” terms, if applicable, and [[File:T27.jpg]] is from either HKF or as described in 2002 paper for organic component. | ||
+ | |||
+ | This was former Tip85 | ||
+ | |||
+ | [[Category:Tips]] [[Category:Thermodynamics]] [[Category:Former Tips]] |
Latest revision as of 08:00, 11 July 2016
In UNIQUAC term, the excess molar volume, , is assumed to be analogous to that of the excess Gibbs energy, i.e.
where is a different interaction parameter from that of
in the
model.
The symmetrically normalized
(subscript UNIQ is omitted in the following text) needs to be converted to the unsymmetrically normalized value (
) for density calculations in MSE.
Conversion from
to
:
Standard state chemical potentials in the two normalizations are related by
(or
)
which is derived from equality of chemical potentials in two normalizations, and using
1 in the infinite dilution limit. Derivatives of ’s with respect to pressure give volumes, i.e.
->
Here is how to calculate
Analogous to
,
can be defined as
and derived from Eq. (1) as:
(2a)
Now, can be calculated from Eq. (3) by combining Eq (1) and (2b):
In Eq. (1) and (2),
(Correspond to D0JI, D1JI, D2JI)
Equation (3) is equivalent to the equation:
Solution volume is then calculated by
Here is calculated from contributions of UNIQUAC and “middle-range” terms, if applicable, and
is from either HKF or as described in 2002 paper for organic component.
This was former Tip85