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Activity Coefficient Models

Activity coefficient models

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• Why activity coefficient models are important?

• A short review on activity coefficient models

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• Application of Activity coefficient models

• Calculation of solubility• Experimental determination of solubility is time consuming and costly

• Therefore it is effective to use activity coefficient models to predict solubility

• In Equilibrium:• Solubility can be calculated as follow

• Is activity of solid which is function of physical properties of solid like melting temperature, heat of fusion and heat capacity

• is activity coefficient

solidax

solida

solid solute sat sata a x

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• Application of Activity coefficient models

• Calculation of Driving force• 1 is in under saturated region• 2 is on saturation curve • 3 is in supersaturated region• 4 is corresponding concentration of point 3 In saturation curve• Driving force is difference in chemical potential Between point 3 and 4

• Calculation of Thermodynamic properties: The derivation of activity coefficient Respect to temperature and concentration should be known. Example -vant hoff enthalpy of solution

x

T

123

4

Driving force

3 3 2 33 3

4 4 4 4

ln lnx x

RT RTx x

( ,T)f x

2

ln

ln ln( , ,...)

vh

vh

x H

T RT

H fT x

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• Activity coefficient models

• Correlative: Wilson,UNIQUAC• Predictive: UNIFAC• Semi-predictive: NRTL-SAC

Experimental and predicted solubility for Lovastatin in solvents using UNIFAC and NRTL-SAC models

Wilson(1964)

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• Very simple model for calculation of activity coefficient for solid liquid Equilibria• Applicable in slightly non-ideal systems• Is not applicable to electrolyte pharmaceutical compound • Good performance in solution Containing alcohols• Two adjustable parameter related to the pure component molar volumes and characteristic energy differences• Molar volume of drug compounds at the solution temperature is often not available• Binary interaction parameter in this model has not physical meaning

Mole fraction solubility of nicotinamide in different puresolvents

UNIQAC(1978)

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• The Universal QUAsi Chemical (UNIQUAC) • Relatively simple because it requires only two adjustable parameters• The activity coefficient is calculated based on combinatorial and residual parts• knowledge of the combinatorial term for complex drug compounds, is often not available• Parameters of combinatorial part can be calculated using group contribution methods• The binary interaction parameter in this model has not physical meaning.• Use of this model requires the determination of binary interaction parameters from

phase equilibrium data for each of the solute-solvent and solvent-solvent binary mixtures

solubility of ranitidine hydrochloride solid forms in isopropanol.

• UNIFAC

• UNIFAC:UNIQUAC Functional group Activity Coefficient• Basic idea: whereas there are thousands of chemical compounds of interest in

chemical technology, the number of functional groups which constitute these compounds is much smaller

• Physical property of a fluid is the sum of contributions made by the molecule's functional groups

• The fundamental assumption of a group-contribution method is additivity; the Contribution made by one group is assumed to be independent of that made by another group.

• This assumption is valid only when the influence of any one group in a molecule is not affected by the nature of other groups within that molecule

• Parameters for about 30 different functional groups are determined simultaneously in an extensive optimization where the total deviation between the UNIFAC model and huge amounts of experimental data is minimized.

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• UNIFAC

• Complex parameterizing: parameter values are primarily correlation values rather than describing the actual physics in each particular interaction

• This limits the possibility to extrapolate the use into new situations• Advantages• Prediction capability• Powerful in predicting solubility in systems with average molecular weights of

100g/mol• Disadvantages• Incapability for prediction of solubility of compounds with molecular weight of

200-600g/mol with complex chemical structure• Pharmaceutical functional group is not defined for UNIFAC or the functional group

additivity become invalid• Is not applicable for isomers• Is not applicable to electrolyte solutes

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• NRTL-SAC

• NRTL-SAC:NRTL-Segment Activity Coefficient• Based on the polymer NRTL model a derivative of the original NRTL model of

Renon and Prausnitz• Non-ideality is because of interactions between three pairwise interacting

conceptual segments: hydrophobic segment, hydrophilic segment, and polar segment

• Hydrophobicity X, polarity Y, and hydrophilicity Z• Hydrophilic segment simulates polar molecular surfaces that are “hydrogen bond

donor or acceptor.“ it represents molecular surfaces with the tendency to form a hydrogen bond

• Hydrophobic segment simulates molecular surfaces with the adversity to form a hydrogen bond

• The polar segment simulates polar molecular surfaces that are “electron pair donor or acceptor

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• NRTL-SAC

• For monosegment solvent component, the NRTL-SAC model reduces to NRTL model.• X, Y, and Z, are to be determined not from the molecular structure but from the interaction characteristics of the molecules in solution.• Available experimental data are used to identify molecular parameters for the solutes, and the model is used to extrapolate to other solvent systems.

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Experimental and predicted solubility for Lovastatin in solvents using UNIFAC and NRTL-SAC models

• NRTL-SAC

• Reference solvents: water-hydrophilic, (X=0,Y,=0Z=1) hexane hydrophobic(Z=0,X=1,Y=0), acetonitrile-polar(X,Z=0,Y=1)

• Binary interaction parameters between segments are calculated using LLE and VLE data in 25 C

• For each solvent, there can be up to four molecular parameters, i.e., X, Y-, Y+, and Z

• Often only one or two molecular parameters are needed for most solvents• Alkanes are hydrophobic: just hydrophobic segment: X• Alcohols are hybrids of hydrophobic and hydrophilic segments and : X and Z• Ketones, esters, and ethers are polar molecules with varying degrees of

hydrophobic contents: X and Y’s.• Solvent molecular parameters: regression of available experimental VLE or LLE data

for Binary systems of solvent and the reference molecules (i.e., hexane, acetonitrile, and water)

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• NRTL-SAC

• Advantages• capability to predict organic electrolyte system• Capability to predict solubility in new solvents• High accuracy in comparison to other activity coefficient models

• Disadvantages• Four adjustable parameters in some systems• This model doe not account for effect of temperature on activity

coefficient

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• Future Works

• Measuring solubility of Oxatomide in organic solvents

• Modification of NRTL-SAC model for accounting effect of temperature on activity coefficient

• Determination of melting temperature, heat of fusioin and heat capacity using DSC

• Modeling of solubility of oxatomide using modified NRTL-SAC model

• Changing the reference solvents in NRTL-SAC model and comparing the results

• Considering three term for

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( 0, , ( ))pC q q r T Tm

Thank you

Any question?

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