(37c) Apparatus to Characterize Liquid-Liquid-Vapor Equilibrium of Polymer-Alkane-CO2 Ternary Mixture Confirms PC-SAFT Predictions Fitted Only to Binary Data

Liquid-liquid-vapor equilibrium (LLVE), predicted only to occur in ternary mixtures of polymer, solvent, and vapor[1], presents special opportunities for supercritical extraction of solvent[2] and pathways to lower barriers of bubble nucleation[3]. While theoretical predictions for LLVE in specific ternary mixtures abound[4], experimental measurements are scarce. Most use some combination of cloud-point measurements, which can be imprecise and hysteretic for viscous polymers, and painstaking analysis of the compositions for each sample of polymer-containing phases[5,6]. We present an efficient and robust method for theoretically predicting and experimentally testing LLVE in polymer-solvent-vapor mixtures.

Due to their importance in polyurethane foaming, we studied mixtures of a polypropylene-glycol-based polyol (PPG), cyclopentane (C5), and carbon dioxide (CO2) at pressures up to 7.5 MPa between 293-333 K. We first developed a model of LLVE based on perturbed chain statistical associating fluid theory (PC-SAFT) fitted to binary coexistence parameters. We then designed an apparatus to reach the predicted LLVE conditions and provide samples of CO2-rich and polymer-rich phases suitable for analysis with gas chromatography (GC). By inferring the composition of the third phase, we demonstrated LLVE under the predicted conditions and found good agreement with the predicted compositions. This efficient and robust method for mapping LLVE in polymer-solvent-gas mixtures opens the way to characterize LLVE across a broad class of polymers and solvents to validate theoretical predictions, enhance supercritical fluid processes, and understand the unique phase behavior near the critical point.

THEORETICAL AND EXPERIMENTAL METHODS

Following the approach of Lindvig et al.[7], we first fit the parameters of our PC-SAFT model to measurements of solubility of CO2 in PPG with the gravimmetry and axisymmetric drop-shape analysis (G-ADSA) method developed by Prof. Di Maio at the University of Naples[8]. Concurrent interfacial tension measurements matched predictions using density functional theory (DFT) based on the model parameters, validating the generalizability of the fit.

We designed our apparatus at the Dow Lake Jackson TXINN Facility for pressures up to 7.5 MPa, minimal sampling volume, and sampling of both volatile (C5 and CO2) and non-volatile (PPG) components. We used a Parr reactor of PPG and C5, to which we added additional CO2 and C5 using an ISCO pump to change the composition in situ. With the gas-sampling port, we sampled the lightest, CO2-rich phase directly into a GC column. A custom dip tube sampled the bottom of the densest, polyol-rich phase, which was collected in the piston of a high-pressure liquid injection system (HPLIS) to vaporize the volatile C5 and CO2 into a GC column with a flash of heat. We repeated each measurement at least twice since sample volumes were small enough not to perturb the equilibrium (i.e., did not change the temperature or pressure beyond the resolution of the instrument). The density of the polyol was inferred using measurements of the density of PPG-CO2 mixtures from G-ADSA and the known density of pure liquid C5.

RESULTS

Our experimental measurements of composition quantitatively agreed with the tie lines predicted by our PC-SAFT model in vapor-liquid, liquid-liquid, and vapor-liquid-liquid equilibria. We demonstrated the emergence of a third phase of intermediate density between the polymer- and CO2-rich phases within an industrially relevant temperature and pressure window. Because we only sampled the lightest and densest phases, we inferred the composition of the intermediate third phase by subtracting the mass of each component calculated to be in the two sampled phases from the known masses added to the reactor. Example results are shown in the attached figure.

APPLICATION

Designing our apparatus and measurements based on an empirical PC-SAFT model significantly facilitates the mapping of an LLVE. This could allow more researchers to fill the wide gap in the literature of LLVE data to build and test models of polymer-solvent-gas mixtures used to optimize supercritical fluid processes. Additionally, using parameters fitted from the data we collected, we have developed a model using the string method applied to DFT to predict the nucleation barrier for bubble nucleation during foaming. Our model predicts that the nucleation barrier could be lowered significantly by first nucleating through liquid-liquid separation under conditions used for polyurethane foaming, a pathway previously only explored in PS-CO2 and PMMA-CO2 at more than three times the pressures[3]. Increased bubble nucleation can dramatically increase the cell density in polyurethane foams, which is essential to reduce the thermal conductivity of polyurethane foams used in refrigeration and building insulation for more energy-efficient temperature control.

REFERENCES

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3. Xu, X.; Cristancho, D. E.; Costeux, S.; Wang, Z.-G. Phys. Chem. Lett. 2013, 4 (10), 1639–1643.
4. Xiong, Y.; Kiran, E 1994, 35 (20), 4408–4415.
5. Seckner, A. J.; McClellan, A. K.; McHugh, M. A. AIChE J. 1988, 34 (1), 9-16
6. Bungert, B.; Sadowski, G.; Arlt, W. Fluid Phase Equilib. 1997, 139 (1–2), 349–359.
7. Lindvig, T.; Michelsen, M. L.; Kontogeorgis, G. M. Eng. Chem. Res. 2004, 43, 1125–1132.
8. Peters, F. T.; Laube, F. S.; Sadowski, G. Fluid Phase Equilib. 2012, 324, 70–79.
9. Giovanna Pastore Carbone, E. Di Maio, S. Iannace, and G. Mensitieri, Polym. Test. 2011, 30, 303.

ACKNOWLEDGEMENTS

This material is based upon work supported by the Dow University Partnership Initiative and by the National Science Foundation Graduate Research Fellowship under Grant No. DGE‐1745301.

FIGURE CAPTION

a) A ternary phase diagram shows theoretical predictions of liquid-vapor equilibrium, liquid-liquid-vapor equilibrium (shaded orange with vertices indicated by stars), and liquid-liquid equilibrium, with example experimental measurements shown by the filled circles. Tie lines are shown by thin black lines. Inset: A magnified view of the CO2-rich vertex showing that the GC measurement (circle) matches the predicted composition of the CO2-rich phase in the liquid-liquid-vapor coexistence (star). b) predicted ratios of the three-phases in the reactor based with densities are given in g/mL. The "3rd phase" is inferred.