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'''MOSCED'''<ref name=Eckert>{{cite journal|author=Thomas .E.R., Eckert C.A.|year=1984|title=Prediction of Limiting Activity Coefficients by a Modified Separation of Cohesive Energy Density Model and UNIFAC|journal=Ind. Eng. Chem. Proc. Dev.|volume=23|pages=194–209}}</ref>  
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<ref name=Lazzaroni>{{cite journal|author=Lazzaroni M. J., Bush D., Eckert C. A., Frank T. C., Gupta S., Olson J. D.|year=2005|title=Revision of MOSCED Parameters and Extension to Solid Solubility Calculations|journal=Ind. Eng. Chem. Res.|volume=44|pages=4075–4083}}</ref> (short for “'''Mo'''dified '''S'''eparation of '''C'''ohesive '''E'''nergy '''D'''ensity Model”) is a thermodynamic model for the estimation of limiting [[activity coefficient]]s (also known as activity coefficient at infinite dilution). From a historical point of view MOSCED can be regarded as an improved modification of the [[Hansen solubility parameter|Hansen method]] and the [[Hildebrand solubility parameter|Hildebrand]] solubility model. The first publication is from 1984 and a major revision of parameters has been done 2005. This revised version is described here.
 
== Basic principle ==
[[File:MOSCEDDerviations.png|thumb|Deviations Chart]]
MOSCED uses component-specific parameters describing electronic properties of a compound. These five properties are partly derived from experimental values and partly fitted to experimental data. In addition to the five electronic properties the model uses the molar volume for every component.
 
These parameters are then entered in several equations to obtain the limiting activity coefficient of an infinitely diluted solute in a solvent. These equations have further parameters which have been found empirically.
 
The authors<ref name=Lazzaroni /> found an average absolute deviation of 10.6% against their database of experimental data. The database contains limiting activity coefficients of binary systems of non-polar, polar and hydrogen compounds, but no water. As can be seen in the deviation chart, the systems with water deviate significantly.
 
== Equations ==
<math>
\ln \gamma_2^{\infty } =
\frac{\nu_2}{RT}
\left[
\left( \lambda_1 - \lambda_2 \right)^2 +
\frac{q_1^2 q_2^2 \left( \tau_1^T - \tau_2^T \right)^2}{\psi_1} +
\frac{\left( \alpha_1^T - \alpha_2^T \right) \left( \beta_1^T - \beta_2^T \right)}{\xi_1}
\right] + d_{12}
</math>
 
<math>
d_{12} = \ln \left( \frac{\nu_2}{\nu_1} \right)^{aa} + 1 + \left( \frac{\nu_2}{\nu_1} \right)^{aa}
</math>
 
<math>
aa = 0.953 - 0.002314 \left( \left( \tau_2^T \right)^2 + \alpha_2^T \beta_2^T \right)
</math>
 
<math>
\alpha^T = \alpha \left( \frac{293 K}{T} \right)^{0.8}
</math>,
<math>
\beta^T = \beta \left( \frac{293 K}{T} \right)^{0.8}
</math>,
<math>
\tau^T = \tau \left( \frac{293 K}{T} \right)^{0.4}
</math>
 
<math>
\psi_1 = POL + 0.002629 \alpha_1^T \beta_1^T
</math>
 
<math>
\xi_1 = 0.68 \left( POL - 1 \right) +
\left[3.4 - 2.4
\exp \left( -0.002687 \left( \alpha_1 \beta_1 \right)^{1.5} \right)
\right]^{\left( 293 K/T \right)^2}
</math>
 
<math>
POL = q_1^4 \left[ 1.15 - 1.15 \exp \left( -0.002337 \left( \tau_1^T\right)^3 \right) \right] + 1
</math>
 
with
 
{| class="wikitable" border="0"
! Parameter!! Description
|-
| ν || Molar liquid volume
|-
| λ || Dispersion parameter
|-
| q|| Induction parameter
|-
| τ|| Polarity parameter
|-
| α|| Hydrogen-bond acidity parameter
|-
| β|| Hydrogen-bond basicity parameter
|-
| ξ and ψ|| Asymmetry factors
|-
| d<sub>12</sub>|| Combinatorial term (modified Flory-Huggins)
|-
| Index 1|| [[Solvent]]
|-
| Index 2|| [[Solute]]
|}
 
Important note: The value 3.4 in the equation for ξ is different from the value 3.24 in the original publication. The 3.24 has been verified to be a typing error.<ref>Sumnesh Gupta: “Our recommendation is to use 3.4 in the MOSCED equation.”</ref>
 
The activity coefficient of the solute and solvent can be extended to other concentrations by applying the principle of the [[Margules_activity_model|Margules equation]]. This gives:
 
<math>
\ln \gamma_2 = \left( \ln \gamma_2^\infty + 2 \left(  \ln \gamma_1^\infty - \ln \gamma_2^\infty \right)  \Phi_2 \right) \Phi_1^2
</math>
 
<math>
\ln \gamma_1 = \left( \ln \gamma_1^\infty + 2 \left(  \ln \gamma_2^\infty - \ln \gamma_1^\infty \right)  \Phi_1 \right) \Phi_2^2
</math>
 
where
 
<math>
\Phi_i= \frac{x_i \nu_i}{\sum_j \nu_j x_j}
</math>
 
is the volume fraction and <math>x_i</math> the mole fraction of compound i.
The activity coefficient of the solvent is calculated with same equations, but interchanging indices 1 and 2.
 
==Model parameters==
The model uses five component specific properties to characterize the interaction forces between a solute and its solvent. Some of these properties are derived from other known component properties and some are fitted to experimental data obtained from data banks.
 
=== Liquid molar volume ===
The molar liquid [[volume]] ν is given in cm³/mol and assumed to be temperature-independent.
 
=== Dispersion parameter ===
The disperson parameter λ describes the [[polarizability]] of a molecule.
 
=== Polarity parameter ===
The polarity parameter τ describes the fixed [[dipole]] of a molecule.
 
=== Induction parameter ===
The induction parameter q describes the effects of induced dipoles (induced by fixed dipoles).
For structures with an aromatic ring the value is set to 0.9, for aliphatic rings and chains this value is set on 1.  
For some compounds the q-parameter is optimized between 0.9 and 1 (e.g. hexene, octene).
 
=== Acidity and basicity parameters===
These parameters describe the effects of [[hydrogen-bonding]] during solving and [[Association (chemistry)|association]].
 
=== Parameter table ===
{| class="wikitable sortable"
|-
! scope="col" |Name
! scope="col" class="unsortable" |ν
! scope="col" class="unsortable" |λ
! scope="col" class="unsortable" |τ
! scope="col" class="unsortable" |q
! scope="col" class="unsortable" |α
! scope="col" class="unsortable" |β
|-
||[[propane]]||                              75.7||      13.10||      0.00||      1.00||      0.00||      0.00
|-
||[[1-phenyl-1-butanone]]||                  145.2||      16.46||      4.98||      1.00||      0.88||      6.54
|-
||[[butane]]||                              96.5||      13.70||      0.00||      1.00||      0.00||      0.00
|-
||[[acetophenone]]||                        117.4||      16.16||      6.50||      0.90||      1.71||      7.12
|-
||[[pentane]]||                              116.0||      14.40||      0.00||      1.00||      0.00||      0.00
|-
||[[epsilon-caprolactone]]||                106.8||      16.42||      9.65||      1.00||      0.43||      13.06
|-
||[[isopentane]]||                          117.1||      13.87||      0.00||      1.00||      0.00||      0.00
|-
||[[dichloromethane]]||                      64.4||      15.94||      6.23||      0.96||      3.98||      0.92
|-
||[[cyclopentane]]||                        94.6||      16.55||      0.00||      1.00||      0.00||      0.00
|-
||[[chloroform]]||                          80.5||      15.61||      4.50||      0.96||      5.80||      0.12
|-
||[[hexane]]||                              131.4||      14.90||      0.00||      1.00||      0.00||      0.00
|-
||[[carbon tetrachloride]]||                97.1||      16.54||      1.82||      1.01||      1.25||      0.64
|-
||[[cyclohexane]]||                          108.9||      16.74||      0.00||      1.00||      0.00||      0.00
|-
||[[1,1-dichloroethane]]||                  84.7||      16.77||      6.22||      0.92||      3.28||      1.56
|-
||[[methylcyclopentane]]||                  113.0||      16.10||      0.00||      1.00||      0.00||      0.00
|-
||[[1,2-dichloroethane]]||                  79.4||      16.60||      6.58||      0.94||      2.42||      1.34
|-
||[[3-methylpentane]]||                      130.4||      14.68||      0.00||      1.00||      0.00||      0.00
|-
||[[1,1,1-trichloroethane]]||                100.3||      16.54||      3.15||      1.01||      1.05||      0.85
|-
||[[2-methylpentane]]||                      132.9||      14.40||      0.00||      1.00||      0.00||      0.00
|-
||[[trichloroethylene]]||                    90.1||      17.19||      2.96||      1.00||      2.07||      0.21
|-
||[[2,3-dimethylbutane]]||                  131.2||      14.30||      0.00||      1.00||      0.00||      0.00
|-
||[[1-chlorobutane]]||                      105.1||      15.49||      3.38||      1.00||      0.11||      1.17
|-
||[[2,2-dimethylbutane]]||                  133.7||      13.77||      0.00||      1.00||      0.00||      0.00
|-
||[[chlorobenzene]]||                        102.3||      16.72||      4.17||      0.89||      0.00||      2.50
|-
||[[heptane]]||                              147.0||      15.20||      0.00||      1.00||      0.00||      0.00
|-
||[[bromoethane]]||                          75.3||      15.72||      4.41||      1.00||      0.22||      1.56
|-
||[[methylcyclohexane]]||                    128.2||      16.06||      0.00||      1.00||      0.00||      0.00
|-
||[[bromobenzene]]||                        105.6||      17.10||      4.29||      0.89||      0.00||      3.13
|-
||[[cycloheptane]]||                        121.7||      17.20||      0.00||      1.00||      0.00||      0.00
|-
||[[iodomethane]]||                          62.7||      19.13||      4.21||      1.00||      1.16||      0.83
|-
||[[3-methylhexane]]||                      146.4||      14.95||      0.00||      1.00||      0.00||      0.00
|-
||[[diiodomethane]]||                        81.0||      21.90||      5.19||      1.00||      2.40||      2.08
|-
||[[2,2-dimethylpentane]]||                  148.9||      14.26||      0.00||      1.00||      0.00||      0.00
|-
||[[iodoethane]]||                          93.6||      17.39||      3.58||      1.00||      0.51||      1.96
|-
||[[2,4-dimethylpentane]]||                  150.0||      14.29||      0.00||      1.00||      0.00||      0.00
|-
||[[acetonitrile]]||                        52.9||      13.78||      11.51||      1.00||      3.49||      8.98
|-
||[[2,3,4-trimethylpentane]]||              159.5||      14.94||      0.00||      1.00||      0.00||      0.00
|-
||[[propionitrile]]||                      70.9||      14.95||      9.82||      1.00||      1.08||      6.83
|-
||[[octane]]||                              163.4||      15.40||      0.00||      1.00||      0.00||      0.00
|-
||[[butyronitrile]]||                        87.9||      14.95||      8.27||      1.00||      0.00||      8.57
|-
||[[2,2,4-trimethylpentane]]||              165.5||      14.08||      0.00||      1.00||      0.00||      0.00
|-
||[[benzonitrile]]||                        103.0||      15.43||      8.21||      0.90||      0.15||      7.41
|-
||[[ethylcyclohexane]]||                    143.0||      16.34||      0.00||      1.00||      0.00||      0.00
|-
||[[glutaronitrile]]||                      95.8||      15.12||      12.59||      1.00||      3.76||      9.11
|-
||[[cyclooctane]]||                          134.9||      17.41||      0.00||      1.00||      0.00||      0.00
|-
||[[nitromethane]]||                        54.1||      13.48||      12.44||      1.00||      4.07||      4.01
|-
||[[2,5-dimethylhexane]]||                  165.6||      14.74||      0.00||      1.00||      0.00||      0.00
|-
||[[nitroethane]]||                          72.0||      14.68||      9.96||      1.00||      1.19||      4.72
|-
||[[nonane]]||                              179.6||      15.60||      0.00||      1.00||      0.00||      0.00
|-
||[[1-nitropropane]]||                      89.5||      15.17||      8.62||      1.00||      0.28||      5.83
|-
||[[decane]]||                              195.8||      15.70||      0.00||      1.00||      0.00||      0.00
|-
||[[2-nitropropane]]||                      90.6||      14.60||      8.30||      1.00||      0.55||      3.43
|-
||[[dodecane]]||                            228.6||      16.00||      0.00||      1.00||      0.00||      0.00
|-
||[[nitrobenzene]]||                        102.7||      16.06||      8.23||      0.90||      0.98||      3.29
|-
||[[tetradecane]]||                          261.3||      16.10||      0.00||      1.00||      0.00||      0.00
|-
||[[dimethylformamide]] (DMF)||                                  77.4||      15.95||      9.51||      1.00||      1.22||      22.65
|-
||[[hexadecane]]||                          294.2||      16.20||      0.00||      1.00||      0.00||      0.00
|-
||[[N,N-dibutylformamide]]||                182.0||      15.99||      5.02||      1.00||      0.24||      14.07
|-
||[[squalane]]||                            526.1||      14.49||      0.00||      1.00||      0.00||      0.00
|-
||[[N,N-dimethylacetamide]]||                93.0||      15.86||      9.46||      1.00||      0.00||      21.00
|-
||1-[[pentene]]||                            110.3||      14.64||      0.25||      0.90||      0.00||      0.24
|-
||[[N,N-diethylacetamide]]||                124.5||      15.66||      6.71||      1.00||      0.25||      18.67
|-
||[[1-hexene]]||                            125.8||      15.23||      0.22||      0.93||      0.00||      0.29
|-
||[[N-methylformamide]]||                    59.1||      15.55||      8.92||      1.00||      8.07||      22.01
|-
||[[1-octene]]||                            157.8||      15.39||      0.44||      0.95||      0.00||      0.51
|-
||[[N-methylacetamide]]||                    76.9||      16.22||      5.90||      1.00||      5.28||      23.58
|-
||[[α-pinene]]||                        159.0||      17.32||      0.15||      0.95||      0.00||      1.30
|-
||[[N-ethylacetamide]]||                    94.3||      16.07||      4.91||      1.00||      4.14||      22.45
|-
||[[benzene]]||                              89.5||      16.71||      3.95||      0.90||      0.63||      2.24
|-
||[[aniline]]||                              91.6||      16.51||      9.41||      0.90||      6.51||      6.34
|-
||[[toluene]]||                              106.7||      16.61||      3.22||      0.90||      0.57||      2.23
|-
||[[2-pyrrolidone]]||                        76.8||      16.72||      11.36||      1.00||      2.39||      27.59
|-
||[[p-xylene]]||                            123.9||      16.06||      2.70||      0.90||      0.27||      1.87
|-
||[[N-methylpyrrolidone]] (NMP)||                  96.6||      17.64||      9.34||      1.00||      0.00||      24.22
|-
||[[ethylbenzene]]||                        122.9||      16.78||      2.98||      0.90||      0.23||      1.83
|-
||[[1-ethylpyrrolidin-2-one]]||              114.1||      16.74||      8.31||      1.00||      0.00||      20.75
|-
||[[isopropylbenzene]]||                    139.9||      17.09||      3.23||      0.90||      0.20||      2.57
|-
||[[1,5-dimethyl-2-pyrrolidinone]]||        115.2||      16.50||      8.45||      1.00||      0.00||      22.66
|-
||[[butylbenzene]]||                        156.6||      17.10||      2.51||      0.90||      0.10||      1.83
|-
||[[N-formylmorpholine]]||                  100.6||      16.10||      10.91||      1.00||      2.42||      19.29
|-
||[[methanol]]||                            40.6||      14.43||      3.77||      1.00||      17.43||      14.49
|-
||[[pyridine]]||                            80.9||      16.39||      6.13||      0.90||      1.61||      14.93
|-
||[[ethanol]]||                              58.6||      14.37||      2.53||      1.00||      12.58||      13.29
|-
||[[2,6-dimethylpyridine]]||                116.7||      15.95||      4.16||      0.90||      0.73||      13.12
|-
||[[1-propanol]]||                          75.1||      14.93||      1.39||      1.00||      11.97||      10.35
|-
||[[quinoline]]||                            118.5||      16.84||      5.96||      0.90||      2.17||      12.10
|-
||[[2-propanol]]||                          76.8||      13.95||      1.95||      1.00||      9.23||      11.86
|-
||[[sulfolane]]||                            95.3||      16.49||      12.16||      1.00||      1.36||      13.52
|-
||[[1-butanol]]||                            92.0||      14.82||      1.86||      1.00||      8.44||      11.01
|-
||[[dimethyl sulfoxide]] (DMSO)||                                71.3||      16.12||      13.36||      1.00||      0.00||      26.17
|-
||[[2-butanol]]||                            92.0||      14.50||      1.56||      1.00||      8.03||      10.21
|-
||[[dioxane]]||                              85.7||      16.96||      6.72||      1.00||      0.00||      10.39
|-
||[[2-methyl-2-propanol]]||                  94.7||      14.47||      2.55||      1.00||      5.80||      11.93
|-
||[[tetrahydrofuran]]||                      81.9||      15.78||      4.41||      1.00||      0.00||      10.43
|-
||[[2-methyl-1-propanol]]||                  92.9||      14.19||      1.85||      1.00||      8.30||      10.52
|-
||[[diethyl ether]]||                        104.7||      13.96||      2.79||      1.00||      0.00||      6.61
|-
||[[1-pentanol]]||                          108.5||      15.25||      1.46||      1.00||      8.10||      9.51
|-
||[[dipropyl ether]]||                      137.6||      15.20||      2.00||      1.00||      0.00||      5.25
|-
||[[1-hexanol]]||                            125.2||      15.02||      1.27||      1.00||      7.56||      9.20
|-
||[[dibutyl ether]]||                        170.4||      15.13||      1.73||      1.00||      0.00||      5.29
|-
||[[1-octanol]]||                            158.2||      15.08||      1.31||      1.00||      4.22||      9.35
|-
||[[diisopropyl ether]]||                    141.8||      14.72||      1.90||      1.00||      0.00||      6.39
|-
||[[phenol]]||                              88.9||      16.66||      4.50||      0.90||      25.14||      5.35
|-
||[[methyl tert-butyl ether]]||              119.9||      15.17||      2.48||      1.00||      0.00||      7.40
|-
||[[benzyl alcohol]]||                      103.8||      16.56||      5.03||      1.00||      15.01||      6.69
|-
||[[anisole]]||                              109.2||      16.54||      5.63||      0.90||      0.75||      3.93
|-
||[[3-Methylphenol|3-methylphenol]] (m-cresol)||                            105.0||      17.86||      4.16||      0.90||      27.15||      2.17
|-
||[[tetraethylene glycol dimethyl ether]]||  221.1||      16.08||      6.73||      1.00||      0.00||      13.53
|-
||[[2-ethoxyethanol]]||                      97.3||      15.12||      7.39||      1.00||      3.77||      16.84
|-
||[[acetic acid]]||                          57.6||      14.96||      3.23||      1.00||      24.03||      7.50
|-
||[[methyl acetate]]||                      79.8||      13.59||      7.54||      1.00||      0.00||      8.38
|-
||[[dimethyl carbonate]]||                  84.7||      17.81||      8.05||      1.00||      0.00||      7.32
|-
||[[ethyl acetate]]||                        98.6||      14.51||      5.74||      1.00||      0.00||      7.25
|-
||[[acetaldehyde]]||                        56.5||      13.76||      8.48||      1.00||      0.00||      6.50
|-
||[[propyl acetate]]||                      115.8||      13.98||      5.45||      1.00||      0.00||      7.53
|-
||[[butanal]]||                              90.4||      15.11||      5.97||      1.00||      0.00||      5.27
|-
||[[butyl acetate]]||                        132.0||      15.22||      4.16||      1.00||      0.00||      6.40
|-
||[[carbon disulfide]]||                    60.6||      19.67||      1.04||      1.00||      0.59||      0.33
|-
||[[benzyl acetate]]||                      142.9||      16.17||      6.84||      0.90||      0.54||      5.53
|-
||[[triethylamine]]||                        139.7||      14.49||      1.02||      1.00||      0.00||      7.70
|-
||[[methyl formate]]||                      62.1||      18.79||      8.29||      1.00||      0.37||      8.62
|-
||[[tributyl phosphate]]||                  345.0||      15.05||      4.87||      1.00||      0.00||      14.06
|-
||[[ethyl benzoate]]||                      144.1||      16.48||      4.97||      1.00||      0.28||      2.40
|-
||[[water]]||                                36.0||      10.58||      10.48||      1.00||      52.78||      15.86
|-
||[[diethyl phthalate]]||                    199.7||      16.33||      6.14||      1.00||      1.07||      7.81
|-
||[[argon]]||                                57.1||      9.84||      0||          1.0||        0||          0   
|-
||[[acetone]]||                              73.8||      13.71||      8.30||      1.00||      0.00||      11.14
|-
||[[oxygen]]||                              52.9||      8.84||      0||          1.0||        0||          0   
|-
||[[2-butanone]]||                          90.2||      14.74||      6.64||      1.00||      0.00||      9.70
|-
||[[nitrogen]]||                            50.0||      7.48||      0||          1.0||        0||          0   
|-
||[[2-pentanone]]||                          107.3||      15.07||      5.49||      1.00||      0.00||      8.09
|-
||[[carbon monoxide]]||                      49.0||      8.15||      0||          1.0||        0||          0   
|-
||[[cyclohexanone]]||                        104.1||      15.80||      6.40||      1.00||      0.00||      10.71
|-
||[[carbon dioxide]]||                      42.2||      8.72||      5.68||      1.0||        1.87||      0   
|-
||[[4-methyl-2-pentanone]]||                125.8||      15.27||      4.71||      1.00||      0.00||      6.34
|-
||[emin][(CF3SO2)2N]||                  258.6||      15.18||      10.72||      0.9||        9.79||      4.75
|-
||[[2-heptanone]]||                          140.7||      14.72||      4.20||      1.00||      0.00||      6.08
|-
||[emmin][(CF3SO2)2N]||                  275.9||      15.25||      10.83||      0.9||        7.20||      5.11
|}
 
== External links ==
* [http://ddbonline.ddbst.de/MOSCEDCalculation/MOSCEDCGI.exe?component1=ethanol&component2=heptane&temperatures=290%20300%20310%20320%20330%20340 Online Calculation of limiting activity coefficients with MOSCED]
 
== References ==
{{reflist}}
 
{{DEFAULTSORT:Mosced}}
[[Category:Thermodynamic models]]

Latest revision as of 01:10, 15 August 2014

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