1、Activity Coefficient Estimation Methods,Bharat Chandramouli February 5, 2002,Activity Coefficient,The activity coefficient is a measure of the non-ideality of mixingTwo components, Enthalpic and Entropic,Estimation/Measurement,Activity coefficients in single component/simple mixtures easy to measure
2、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
3、,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,The activity c
4、oefficient 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
5、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,UNIFAC Methods,Interaction parameters are fit from experimental data This work is still ongoing and many
6、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 activit
7、y coefficient is given by,Molar Volume,Cohesive energy density,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 di
8、lute 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 togetherTheory of cohesive energy developed by Hildebrand for dispersive systems and extended by Hansen for polar and hydrogen bonding,Solubility parameters ar
9、e measures of cohesive energy,solubility parameter,coh. energy density,cohesive energy,Solubility parameter,Calculating solubility parameters,Hansen and others compiled molar attraction constants for functional groups, which are additive contributions to the solubility parameter,Attraction Constants
10、 (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
11、 using component mole fraction and molar volume to get “average om”,Cohesive Energy Density,i,omA can be derived asib 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 Coeffi
12、cient,Putting the two components together,+,ln iom =,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 UN
13、IFAC?,UNIFAC more powerful interaction UNIFAC not universalmissing 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
14、use this?,Water solubility estimationSolvent-Water partitioning (Kow),Gas/Particle Partitioning,What happens when a semivolatile organic (SOC) encounters a particle?,Partitioning Modes,Mode of SOC-particle interaction depends on the particle Adsorption Solid particle, no organic liquid layer (dust,
15、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,Pankow (1994) for absorptive partitioning,fom- fraction extractable organic matter igom - activity coefficient of SOC in om MWom - molecular weight of om,
