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Activity Coefficient Estimation Methods. Bharat Chandramouli February 5, 2002. Activity Coefficient . The activity coefficient is a measure of the non-ideality of mixing Two components, Enthalpic and Entropic. Estimation/Measurement.

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activity coefficient estimation methods

Activity Coefficient Estimation Methods

Bharat Chandramouli

February 5, 2002

activity coefficient
Activity Coefficient
  • The activity coefficient is a measure of the non-ideality of mixing
  • Two components, Enthalpic and Entropic
estimation measurement
  • Activity coefficients in single component/simple mixtures easy to measure
  • Activity coefficients in water or octanol can be calculated from solubility given sufficiently sensitive methods
need for estimation
Need for estimation
  • What about complex mixtures?
  • What about dynamic systems with changing compositions?
  • It becomes more practical to use estimation methods to approximate g in these cases
estimation methods
Estimation Methods
  • Group contribution methods are most common because they have predictive ability
  • There are two group contribution methods commonly used for iom
    • calculation from solubility parameters
    • UNIFAC calculation
unifac the universal functional group activity coefficient model
UNIFAC the UNIversal Functional group Activity Coefficient model
  • The activity coefficient is calculated from two components


(V, SA)

Residual (interactions)

(Experiment Fit)

  • The group contribution components consist of
    • volume contributor -Rk
    • surface area contribution -Qk
    • interaction parameter between functional groups Amk
  • To calculate interactions, similar sub-groups are assigned to groups and interactions are between these groups
  • Calculate activity coefficients by summing all contributions and interactions
unifac simple example
UNIFAC-Simple example
  • Ethanol CH3-CH2-OH
unifac methods
UNIFAC Methods
  • Interaction parameters are fit from experimental data
  • This work is still ongoing and many parameters still not available
hansen solubility parameter
Hansen Solubility Parameter
  • This method calculates activity coefficients from the solubility parameter
  • Theory of cohesive energy developed by Hildebrand for dispersive systems and extended by Hansen for polar and hydrogen bonding
hansen activity coefficient
Hansen Activity Coefficient
  • The activity coefficient is given by

Cohesive energy density

Molar Volume

Size effect term



the size effect term
The Size Effect Term
  • i,omd is a measure of the effect of differing sizes of i and om on their entropy of mixing
  • This was derived by Flory and Huggins using statistical thermodynamics
  • For an infinitely dilute solution
cohesive energy e coh
Cohesive Energy (Ecoh)
  • Closely linked to the heat of evaporation
  • It is a measure of a the ability of a liquid molecule to stay together
  • Theory of cohesive energy developed by Hildebrand for dispersive systems and extended by Hansen for polar and hydrogen bonding
solubility parameter
Solubility parameter
  • Solubility parameters are measures of cohesive energy

cohesive energy

solubility parameter

coh. energy density

calculating solubility parameters
Calculating solubility parameters
  • Hansen and others compiled molar attraction constants for functional groups, which are additive contributions to the solubility parameter
attraction constants f
Attraction Constants (F)
  • The product of V was found to vary linearly across homologous series
  • Additivity of structural sub-groups
  • F=V values compiled for dispersion and polar components of 
  • Hansen later compiled additive contributions to Eh
multi component mixtures
Multi-component Mixtures
  • How are om parameters calculated?
  • Parameters weighted using component mole fraction and molar volume to get “average om”
cohesive energy density
Cohesive Energy Density
  • i,omA can be derived as
  • ib is a weighting factor based on dispersive forces, has been tabulated for a variety of compounds
  • ib corrects for the fact that polar and H bonding forces are localized
activity coefficient1
Activity Coefficient
  • Putting the two components together

lniom =


  • First, calculate group contributions for each component in the mixture
  • Calculate “om” parameters by weighting with mole fraction and molar volume
  • Calculate parameters for compound of interest
  • Calculate activity coefficient
hansen or unifac
Hansen or UNIFAC?
  • UNIFAC more powerful interaction
  • UNIFAC not universal–missing parameters
  • Hansen has certain inconsistencies as certain parameters have to be culled from different sources. Very sensitive to parameter choice
  • ib not widely available for many compounds, so estimation may be difficult
where do you use this
Where do you use this?
  • Water solubility estimation
  • Solvent-Water partitioning (Kow)
gas particle partitioning



Thermodynamic Equilibrium?

Particle type




Gas/Particle Partitioning
  • What happens when a semivolatile organic (SOC) encounters a particle??
partitioning modes
Partitioning Modes
  • Mode of SOC-particle interaction depends on the particle
    • Adsorption Solid particle, no organic liquid layer (dust, inorganic salts)
    • Absorption Particle either liquid, or has substantial liquid layer (combustion particles, secondary organic aerosol)
  • SOCs such as PAHs, and alkanes primarily partition to organic or carbonaceous aerosols rather than to mineral-based aerosols
predictive partitioning models
Predictive Partitioning models
  • Pankow (1994) for absorptive partitioning

fom- fraction extractable organic matter

igom- activity coefficient of SOC in om

MWom-molecular weight of om