(345e) Minimum Free Energy Path for Bubble Nucleation in Compressible Polymer-Carbon Dioxide Mixtures

We studied the bubble nucleation in compressible polymer-carbon dioxide (CO₂) mixtures by combining a newly developed density-functional theory (DFT) with the string method.  The DFT is constructed from a perturbed-chain statistical associating fluid theory equation of state by using the weight density functions of fundamental measure theory.  The additional long-range dispersion contributions are included using a mean-field approach.  We first apply our DFT to the interfacial properties of poly(methyl methacrylate) (PMMA)-CO₂ and polystyrene (PS)-CO₂ mixtures.  The calculated interfacial tension values are in good agreement with experimental data.  The nucleation of PMMA-CO₂ and PS-CO₂ mixtures along the minimum free energy path is then investigated by the string method at several temperatures with different initial pressures up to 50 MPa.  Evolution of the density profiles along the pathway shows that, in the initial stage of bubble formation, the CO₂ density overshoots on its way to the critical nucleus.  The classical nucleation theory using bulk properties and equilibrium interfacial tensions shows huge discrepancy with results from the string method.  However, a modified version of the classical nucleation theory using tension values fitted from the large nuclei shows reasonable agreement.  To obtain a free energy barrier around 20 kT that corresponds to moderately fast nucleation rate, the nucleation temperature for PMMA-CO₂ mixtures has to be higher than 310 K, while it has to be higher than 370 K for PS-CO₂ mixtures.  In the vicinity of triple point, there are two types of critical nucleus with very high nucleation free energy barrier.