Polymer-Solvent Vapor-Liquid Equilibrium: Equations of State versus Activity Coefficient Models

Paola Chanel Villegas Tapia A01373219César Eduardo Flores Ríos A01168336

Mayte Rueda Munguía A01373984Liliana Itzel Romero Ramírez A01551456

Two models There are two basic modeling tools available for the treatment of polymer-solvent mixtures: excess Gibbs free energy (Gex) or activity coefficient models and equation of state (EOS) models.

Gex or activity coefficient models- More flexible to accommodate highly complex phase

behavior

EOS- Can account for compressibility effects in more

consistent way- They are more successful at higher pressures

Equilibrium models

- Classical Flory-Huggins (FH) Gex model.

- Model of Chen, this model combines the combinatorial term of the Flory-Huggins model with the nonrandom two-liquid (NRTL) term

Thermodynamic Background and ModelsIn general, the activity coefficient models are believed to be more flexible to accommodate highly complex phase behavior. The EOS models, on the other hand, can account for compressibility effects in a thermodynamically more consistent way and they are more successful at higher pressures

In this case, you can use some special software like Aspen plus and polymers plus.

Differences between the activity coefficient models and the EOS approach. In general, the activity coefficient models are believed to be more flexible to accommodate highly complex phase behavior.

The EOS models, on the other hand, can account for compressibility effects in a thermodynamically more consistent way, and they are more successful at higher pressures.

The FH model in binary mixtures is:

Volume fractions:

Degree of polymerization:

EOS + G ex (SRK EOSFor the EOS + Gex model, we use the SRK EOS coupled with the FH activity coefficient model in the Huron-Vidal

with temperature and critical pressure

with the temperature-dependent function R as suggested by Mathias and Copeman:

pure component constant used:

for mixturesa & b

Results● The Mathias-Copeman constants are primarily necessary to predict

accurately the pure-component saturation pressure of a component as a function of temperature and polymers do not exhibit measurable vapor pressures.

● Investigators developed correlations for the critical properties of alkanes as a function of the carbon number

● We recognize that using universal Tc and Pc values for all the polymers will not be realistic for all design purposes. Eventually,the values of these constants may have to be selected separately for each polymer considering available pure-component information such as heat capacity, density, and so on.

Results Tc= 1800K Pc= 10 bar

results

For the benzene + polystyrene binary mixture, Hao et al. (1992) reports infinite-dilution activity coefficients at different temperatures and for polymers with different molecular weights. These values scatter somewhat and range from 5 to 8.

Discussion and conclusion ● The equation of state models developed for conventional mixtures can be

extended to quantitatively describe the VLE of polymer-solvent mixtures, if carefully selected parameters are used for the pure polymer.

● The EOS + Gex mixing rules represent an accurate way of describing mixture phase behavior.

● There are extensive VLE data to correlate the model parameters with, it is not justifiable to use multiparameter phase equilibrium models for moderately nonideal polymer-solvent mixtures.

ReferenceHasan O., Costas P., and Chau C. (1998). Polymer-Solvent Vapor-Liquid Equilibrium: Equations of State versus Activity Coefficient Models. Retrieved from http://pubs.acs.org/doi/abs/10.1021/ie970674r?journalCode=iecred

http://pubs.acs.org/doi/abs/10.1021/ie970674r?journalCode=iecredhttp://pubs.acs.org/doi/abs/10.1021/ie970674r?journalCode=iecredhttp://pubs.acs.org/doi/abs/10.1021/ie970674r?journalCode=iecred