MOSCED[1] [2] (short for “Modified Separation of Cohesive Energy Density Model”) is a thermodynamic model for the estimation of limiting activity coefficients (also known as activity coefficient at infinite dilution). The first publication is from 1984 and a major revision of parameters has been done 2005. This revised version is described here.
Basic Principle
editMOSCED 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[2] found an average absolute deviation of 10.6% against their database of experimental data.
Equations
edit
![{\displaystyle \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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a20b15a03933eb57c10dfcd126b594f8758c4fae)
, ,
![{\displaystyle \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(293K/T\right)^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cd333846bf32bb17eb69dcdafde08439ea9a29ad)
![{\displaystyle POL=q_{1}^{4}\left[1.15-1.15\exp \left(-0.002337\left(\tau _{1}^{T}\right)^{3}\right)\right]+1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/63211306ba8d127cbc6afce98afc71e8b8d2e94e)
with
| 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 |
| d12 | Combinatorial term |
| Index 1 | Solute |
| Index 2 | Solvent |
Models Parameters
editThe 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
editThe molar liquid volume ν is given in cm³/mol and assumed to be temperature-independent.
Dispersion Parameter
editThe disperson parameter λ describes the polarizability of a molecule.
Polarity Parameter
editThe polarity parameter τ describes the fixed dipole of a molecule.
Induction parameter
editThe induction parameter q describes the effects of induced dipoles (induced by fixed dipoles).
Acidity and Basicity parameters
editThese parameters describe the effects of hydrogen-bonding during solving and association.
Parameter Table
edit| Name | ν | λ | τ | q | α | 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 |
| propanenitrile | 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 |
| butanenitrile | 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 |
| 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 | 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 |
| 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 |
| 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 |
References
edit- ^ Thomas .E.R., Eckert C.A. (1984). "Prediction of Limiting Activity Coefficients by a Modified Separation of Cohesive Energy Density Model and UNIFAC". Ind. Eng. Chem. Proc. Dev. 23: 194-209.
- ^ a b Lazzaroni M. J., Bush D., Eckert C. A., Frank T. C., Gupta S., Olson J. D. (2005). "Revision of MOSCED Parameters and Extension to Solid Solubility Calculations". Ind. Eng. Chem. Res. 44: 4075-4083.
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