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 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 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 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 activity coefficient is calculated from two components Combinational (V, SA) Residual (interactions) (Experiment Fit)

UNIFAC 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 Ethanol CH3-CH2-OH Main Group. Subgroup Rk (vol) Qk (SA) Amk CH3 “CH2” CH3 (1) 0.9011 0.848 0, 0 CH2 CH2 (2) 0.6744 0.540 OH “OH” OH (2) 1.000 1.200 986.5, 156.4

UNIFAC Methods Interaction parameters are fit from experimental data This work is still ongoing and many parameters still not available

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 The activity coefficient is given by Cohesive energy density Molar Volume Size effect term Enthalpy Entropy

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 (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 parameters are measures of cohesive energy cohesive energy solubility parameter coh. energy density

Calculating solubility parameters Hansen and others compiled molar attraction constants for functional groups, which are additive contributions to the solubility parameter

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 How are om parameters calculated? Parameters weighted using component mole fraction and molar volume to get “average om”

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 Coefficient Putting the two components together ln iom = +

Calculation 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? 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? Water solubility estimation Solvent-Water partitioning (Kow)

Gas/Particle Partitioning What happens when a semivolatile organic (SOC) encounters a particle?? particle gas Thermodynamic Equilibrium? Temperature Humidity Particle type Compound This picture is a simplistic overview of gas/particle partitioning. What we study

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 To go beyond vapor pressure, we first have to consider the mode of partitioning, which depends on the type of particle we are dealing with. Adsorption, where the particles are solid and the SOC interacts with the surface. Or, with liquid particles with a substantial organic layer, the SOC interacts with the liquid layer and the partitioning is more of a bulk phenomenon. Many studies have shown that SOCs tend to partition to organic aerosols to a much greater extent, because Kp values tend to be higher.

Predictive Partitioning models Pankow (1994) for absorptive partitioning This is the model we use to predict partitioning on aerosols with an organic liquid layer. fom- fraction extractable organic matter igom - activity coefficient of SOC in om MWom - molecular weight of om