cosmosac regression presentation
TRANSCRIPT
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Sigma profile generation with
conceptual segment approach
Md Rashedul Islam
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Outline
Background
Objective
Solvation thermodynamics
Conceptual segment idea
Sigma profile generation model formulation
Results and Discussion
Conclusion
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Background
A priori prediction of fluid phase equilibria and liquid phase non-
idealities are key factors in process and product development
Thermodynamic behavior is calculated/predicted based on group-
contribution methods, activity-coefficient models, and solvation-
thermodynamics
Solvation-thermodynamic approach predicts thermo-physical
properties based on molecular structure only
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Motivation
Among the solvation thermodynamic based models, COSMO-RS
and COSMO-SAC are the are well recognized
A key input to these models is so called Sigma Profile, i.e. ahistogram of charge density distribution over molecular surface
Typically -profile is generated using quantum mechanical
calculation
Interested researchers are intimated by the complexity of quantummechanical calculation to use COSMO-based model
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Objective We introduce conceptual segment based concept of NRTL-SAC
activity coefficient model
We select four reference solvents to represents hydrophobic,
solvation, polar, and hydrophilic conceptual segments
We generate -profile of any molecules from the linear
combination of -profile of four reference solvents
We identify the conceptual segment numbers from fitting availablesolubility date involving the molecules and four reference solvents
or their equivalents
We predict the solubility of three drug molecules to validate our
methodology
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Thermodynamic Background
Solubility Thermodynamics
Activity coefficient models:
UNIFAC
NRTL-SAC
COSMO-SAC
Theoretical structure of activity coefficient
=
+
=
= =+
: mole fraction of solute at saturation
: activity coefficient of solute
: heat of fusion of solute
T : melting temperature of solute
: solubility product constant
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NRTL-SAC model
A derivative of NRTL model
A practical thermodynamic framework for solubility modeling Surface interaction characteristics of a molecules are exploited
Qualitative parameters are identified from representative solvents:hydrophobic, polar, and hydrophilic
Due to multiple crystalline structure, multiple melting point or
latent heat of fusion may exist
Ksp is estimated through regression using experimental solubility
NRTL-SAC predicts solubility better than COSMO-SAC does
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Thermodynamic Background
Solubility Thermodynamics
Activity coefficient models:
UNIFAC
NRTL-SAC
COSMO-SAC
Theoretical structure of activity coefficient
=
+
=
= =+
: mole fraction of solute at saturation
: activity coefficient of solute
: heat of fusion of solute
T : melting temperature of solute
: solubility product constant
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Solvation Thermodynamic Model
Predict inter-molecular interactions based on molecularstructure
Characterize liquid phase non-ideality
Computational quantum mechanics is used to predict thermo-
physical properties
Models: COSMO-RS 1and COSMO-SAC2
COSMO-based models require sigma profile as input
Sigma profile is a molecular-specific distribution of surface-
charge density
1. Klamt et al2. Lin and Sandler
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COSMO-SAC Model
COSMO-SAC model predict thermo-physical properties based
on solvation free energy
Solvation free energy represents Gibbs free energy required
to bring a moving molecule from a fixed position in ideal state
to a fixed position in solution
Solvation free energy is related
to activity coefficient
Lin and Sandler, 2002
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Sigma Profile
Sigma profile is a measure of molecules dipole and higher
moment interaction with surrounding medium
Probability distribution of surface-charge density of a
molecule or a mixture, ()
-0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025
0
5
10
15
20
25
30
35
, e/Ang2
P()
*A(),Ang
2
Hexane
DMSO
Nitromethane
Water
Sigma profile of amixture is a weighted
average of the pure
components.
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Merits and Demerits of COSMO-SAC Model
Useful for priori estimates of thermo-physical properties of
new and unmeasured species
Predicts phase equilibria for new mixture
Merits
Sigma profile is highly subjected
to structural conformation
Over and under prediction of
solubility likely observed
Demerits
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Proposed Idea
Conceptual segment, i.e. X,Y+, Y-, and Z, idea from NRTL-SAC
is introduced into COSMO-SAC
Sigma profile is generated from the linear combination of
sigma profile of reference molecules
Like NRTL-SAC, reference molecules are hydrophobic, polar,
and hydrophilic
Cavity volume is calculated from the cavity volume and
conceptual segment parameters
X,Y+, Y-,Z are estimated from experimental solubility
Ksp value is also regressed if necessary
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Parameter Regression Algorithm
Non-linear regression is due to non-linearity of COSMO-SAC
Constrained optimization is employed for non-negativity of
sigma profile
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Results and Discussion
Proposed algorithm is implemented to predict the solubility of
three drug molecules: Caffeine, Aspirin, and Acetaminophen
For each drug, solubility is reported based on the sigma
profile from Virginia Tech(VT) database
Solubility of each drug is calculated from new sigma profile
and reported alongside VT results to demonstrate
improvement
For Acetaminophen, solubility in different binary solvent is
also predicted
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Results and Discussion
Caffeine
0
3
6
9
1215
18
21
24
27
-0.03-0.025-0.02-0.015-0.01-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03
SigmaProfile,P()*Ai
(2)
Screening Charge Density, (e/2)
Sigma Profile of Caffeine
COSMOSAC VT
COSMOSAC-XYZ
Solvent Experimental solubility
N-HEXANE 3.94E-06
2-ETHOXYETHANOL 0.006779
1-OCTANOL 0.002455
1,4-DIOXANE 0.008204
N,N-DIMETHYLFORMAMIDE 0.012558
WATER 0.002247
ETHANOL 0.0017ETHYL-ACETATE 0.00409
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Results and Discussion
Caffeine
Regression ResultsHf & Tm Ksp
X 0 0Y+ 0.4296 0.4675Y- 1.2710 1.2044
Z 0.2553 0.1619Cavity volm 137.88 134.56
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01
Mo
delsolubility,xmodel
Experimental solubility, xexp
Caffeine: COSMOSAC Regression
Hf & Tm
Ksp
VT
Hexane
Water
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Results and Discussion
Aspirin
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00
Modelsolubility,Xmodel
Experimental solubility, Xexp
Aspirin: COSMOSAC Regression
COSMOSAC VT
COSMOSACXYZ
Hf & TmRegression Results
Hf & Tm KspX 0.0357 0.0802
Y+ 0.0837 0.0845Y- 0.6555 0.6281Z 0.5716 0.5869
Cavity volm 74.04 79.10
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Results and Discussion
Acetaminophen (Paracetamol)
0
2
4
6
8
10
12
14
16
18
20
22
-0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03
SigmaProfile,P()*Ai(
2)
Screening Charge Density, (e/2)
Sigma Profile of Acetaminophen
COSMOSAC VTCOSMOSAC-XYZ
XYZKsp
SOLVENT Solubility Mole fractionWATER 17.39 0.002068
METHANOL 371.61 0.073012
ETHANOL 232.75 0.066232
ETHYLENE-GLYCOL 144.3 0.055935
1-PROPANOL 132.77 0.050135
ISOPROPYL-ALCOHOL 135.01 0.050941
N-BUTANOL 93.64 0.043897
1-PENTANOL 67.82 0.038043
1-HEXANOL 49.71 0.038014
1-HEPTANOL 37.43 0.0279671-OCTANOL 27.47 0.023118
ACETONE 111.65 0.041132
METHYL-ETHYL-KETONE 69.99 0.032308
METHYL-ISOBUTYL-KETONE 17.81 0.011663
TETRAHYDROFURAN 155.37 0.069000
1,4-DIOXANE 17.08 0.009857
ETHYL-ACETATE 10.73 0.006215
ACETONITRILE 32.83 0.008836
DIETHYL-AMINE 1316.9 0.389184
N,N-DIMETHYLFORMAMIDE 1012.02 0.328548
DIMETHYL-SULFOXIDE 1132.56 0.369225
ACETIC-ACID 82.72 0.031814
DICHLOROMETHANE 0.32 0.000180
CHLOROFORM
1.54 0.001215
CARBON-TETRACHLORIDE 0.89 0.000905
TOLUENE 0.34 0.000207
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Results and Discussion
Acetaminophen (Paracetamol)
Regression Results4 para. 5 para.
X 0.2980 0.6291Y+ 0.0379 0Y- 0 0
Z 1.3652 1.3142Ksp -3.5364
Cavity volm 82.43 125.75
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00
Modelsolubility,Xmodel
Experimental solubility, Xexp
Acetaminophen: COSMOSAC Regression
COSMOSAC VT COSMOSACXYZ XYZKsp
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Results and Discussion
Hydrophilic-hydrophilic pair
Methanol-water binary Ethanol-water binary
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Results and Discussion
polar-hydrophilic pair
Acetone-water binary 1,4-dioxane-water binary
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Results and DiscussionPolar-hydrophobic pair
Acetone-toluene binary
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Results and DiscussionHydrophilic-hydrophobic pair
Methanol-ethyl acetate binary Ethanol-ethyl acetate binary
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Conclusion
The proposed methodology offers a very simile and practical
approach to generate -profile This method generate -profile of any molecule in terms of
conceptual segment numbers
Conceptual segment numbers are in turn identified by fitting
against experimental solubility data in solvents of various nature
The methodology requires no knowledge of molecular structure nor
molecular conformation and no use of DFT calculations or quantum
chemistry packages
The generated -profile perform well in COSMO-based predictions
of thermophysical properties.
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Reference