# MOSCED

MOSCED (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).[1][2] From a historical point of view MOSCED can be regarded as an improved modification of the Hansen method and the Hildebrand solubility model by adding higher interaction term such as polarity, induction and separation of hydrogen bonding terms. This allows the prediction of polar and associative compounds, which most solubility parameter models have been found to do poorly. In addition to making quantitative prediction, MOSCED can be used to understand fundamental molecular level interaction for intuitive solvent selection and formulation.

In addition to infinite dilution, MOSCED can be used to parameterize excess Gibbs Free Energy model such as NRTL, WILSON, Mod-UNIFAC to map out Vapor Liquid Equilibria of mixture. This was demonstrated briefly by Schriber and Eckert [3] using infinite dilution data to parameterize WILSON equation.

The first publication is from 1984 and a major revision of parameters has been done 2005. This revised version is described here.

## Basic principle

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[2] 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.

Due to such huge deviation of water as solute as seen in the chart, new water parameters are regressed to improve results.[4] All the data for regression were taking from Yaws Handbook of Properties for Aqueous System.[5] Using the old water parameter, for water in organics, Root Mean Square Deviation(RMSD) for ln (γ) was found to be around 2.864% and Average Absolute Error(AAE) for (γ) around 3056.2 %.[4] That is a significant error which might explain the deviation as seen from the graph. With the new water parameters for water in organics, RMSD for ln (γ) decreased to 0.771% and AAE for (γ) also decreased to 63.2%.[4] The revised water parameters can be found in the table below titled "Revised water".

## Equations

${\displaystyle \ln \gamma _{2}^{\infty }={\frac {\nu _{2}}{RT}}\left[\left(\lambda _{1}-\lambda _{2}\right)^{2}+{\frac {q_{1}^{2}q_{2}^{2}\left(\tau _{1}^{T}-\tau _{2}^{T}\right)^{2}}{\psi _{1}}}+{\frac {\left(\alpha _{1}^{T}-\alpha _{2}^{T}\right)\left(\beta _{1}^{T}-\beta _{2}^{T}\right)}{\xi _{1}}}\right]+d_{12}}$
${\displaystyle d_{12}=\ln \left({\frac {\nu _{2}}{\nu _{1}}}\right)^{aa}+1-\left({\frac {\nu _{2}}{\nu _{1}}}\right)^{aa}}$
${\displaystyle aa=0.953-0.002314\left(\left(\tau _{2}^{T}\right)^{2}+\alpha _{2}^{T}\beta _{2}^{T}\right)}$
${\displaystyle \alpha ^{T}=\alpha \left({\frac {\text{293 K}}{T}}\right)^{0.8}}$,
${\displaystyle \beta ^{T}=\beta \left({\frac {\text{293 K}}{T}}\right)^{0.8}}$,
${\displaystyle \tau ^{T}=\tau \left({\frac {\text{293 K}}{T}}\right)^{0.4}}$
${\displaystyle \psi _{1}={\text{POL}}+0.002629\alpha _{1}^{T}\beta _{1}^{T}}$
${\displaystyle \xi _{1}=0.68\left({\text{POL}}-1\right)+\left[3.4-2.4\exp \left(-0.002687\left(\alpha _{1}\beta _{1}\right)^{1.5}\right)\right]^{\left(293K/T\right)^{2}}}$
${\displaystyle {\text{POL}}=q_{1}^{4}\left[1.15-1.15\exp \left(-0.002337\left(\tau _{1}^{T}\right)^{3}\right)\right]+1}$

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 (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.[6]

The activity coefficient of the solute and solvent can be extended to other concentrations by applying the principle of the Margules equation. This gives:

${\displaystyle \ln \gamma _{2}=\left(\ln \gamma _{2}^{\infty }+2\left(\ln \gamma _{1}^{\infty }-\ln \gamma _{2}^{\infty }\right)\Phi _{2}\right)\Phi _{1}^{2}}$
${\displaystyle \ln \gamma _{1}=\left(\ln \gamma _{1}^{\infty }+2\left(\ln \gamma _{2}^{\infty }-\ln \gamma _{1}^{\infty }\right)\Phi _{1}\right)\Phi _{2}^{2}}$

where

${\displaystyle \Phi _{i}={\frac {x_{i}\nu _{i}}{\sum _{j}\nu _{j}x_{j}}}}$

is the volume fraction and ${\displaystyle x_{i}}$ 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 dispersion 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.

### Parameter table

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
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 (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
${\displaystyle {\ce {[emin][(CF3SO2)2N]}}}$ 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
Revised Water 26.60 6.53 14.49 1.00 45.34 12.81
${\displaystyle {\ce {[emmin][(CF3SO2)2N]}}}$ 275.9 15.25 10.83 0.9 7.20 5.11

## References

1. ^ Thomas, Eugene R; Eckert, Charles A (1984). "Prediction of limiting activity coefficients by a modified separation of cohesive energy density model and UNIFAC". Industrial & Engineering Chemistry Process Design and Development. 23 (2): 194–209. doi:10.1021/i200025a002.
2. ^ a b Lazzaroni, Michael J; Bush, David; Eckert, Charles A; Frank, Timothy C; Gupta, Sumnesh; Olson, James D (2005). "Revision of MOSCED Parameters and Extension to Solid Solubility Calculations". Industrial & Engineering Chemistry Research. 44 (11): 4075–83. doi:10.1021/ie049122g.
3. ^ Schreiber, L. B.; Eckert, C. A. (1971-10-01). "Use of Infinite Dilution Activity Coefficients with Wilson's Equation". Industrial & Engineering Chemistry Process Design and Development. 10 (4): 572–576. doi:10.1021/i260040a025. ISSN 0196-4305.
4. ^ a b c Dhakal, Pratik; Paluch, Andrew S (2018-01-08). "Assessment and Revision of the MOSCED Parameters for Water: Application to Limiting Activity Coefficients and Binary Liquid-Liquid Equilibrium". Industrial & Engineering Chemistry Research. 57 (5): 1689–1695. doi:10.1021/acs.iecr.7b04133. ISSN 0888-5885.
5. ^ Yaws, C. L. Yaws' Handbook of Properties for Aqueous Systems; Knovel, 2012.
6. ^ Sumnesh Gupta: “Our recommendation is to use 3.4 in the MOSCED equation.”[This quote needs a citation]