Modeling the Cloud Curves and the Solubility of Gases in Amorphous and Semicrystalline Polyethylene with the SAFT-VR Approach and Flory Theory of Crystallization

Modeling Sorption of Hydrocarbons in Polyethylene with the SAFT-γ Mie Approach Combined with a Statistical-Mechanical Model to Describe Semicrystalline Polymers

A recently developed statistical-mechanical model is applied systematically to estimate the fraction of tie-molecules (polymer chains linking different crystals directly or via entanglements) in semicrystalline polyethylene (PE) samples. The amorphous domains of the polymer are divided into constrained interlamellar domains and "free" outer-lamellar domains. A set of model parameters is assigned to each sample by correlating previous experimental measurements and minimizing the difference between the predicted solubility of pure hydrocarbons in the sample and the experimental values. We show that the sorption isotherms of multiple pure fluids in each sample can be described by a single parameter set, proving that the polymer-solute interactions (described accurately by the SAFT-γ Mie EoS) are decoupled from the sample-specific properties of the polymer. We find that ∼30% of the crystalline stems in the lamellae of PE are connected to tie-molecules, within the bounds suggested by previous theoretical and computational work. The transferability of the sample-specific parameters is assessed by predicting cosolubility effects and solubility at different temperatures, leading to good agreement with experimental data.

On the liquid demixing of water + elastin-like polypeptide mixtures: bimodal re-entrant phase behaviour

Water + elastin-like polypeptides (ELPs) exhibit a transition temperature below which the chains transform from collapsed to expanded states, reminiscent of the cold denaturation of proteins. This conformational change coincides with liquid-liquid phase separation. A statistical-thermodynamics theory is used to model the fluid-phase behavior of ELPs in aqueous solution and to extrapolate the behavior at ambient conditions over a range of pressures. At low pressures, closed-loop liquid-liquid equilibrium phase behavior is found, which is consistent with that of other hydrogen-bonding solvent + polymer mixtures. At pressures evocative of deep-sea conditions, liquid-liquid immiscibility bounded by two lower critical solution temperatures (LCSTs) is predicted. As pressure is increased further, the system exhibits two separate regions of closed-loop of liquid-liquid equilibrium (LLE). The observation of bimodal LCSTs and two re-entrant LLE regions herald a new type of binary global phase diagram: Type XII. At high-ELP concentrations the predicted phase diagram resembles a protein pressure denaturation diagram; possible "molten-globule"-like states are observed at low concentration.

Predicting the Fluid-Phase Behavior of Aqueous Solutions of ELP (VPGVG) Sequences Using SAFT-VR

The statistical associating fluid theory for potentials of variable range (SAFT-VR) is used to predict the fluid phase behavior of elastin-like polypeptide (ELP) sequences in aqueous solution with special focus on the loci of lower critical solution temperatures (LCSTs). A SAFT-VR model for these solutions is developed following a coarse-graining approach combining information from atomistic simulations and from previous SAFT models for previously reported relevant systems. Constant-pressure temperature-composition phase diagrams are determined for solutions of (VPGVG)_n sequences + water with n = 1 to 300. The SAFT-VR equation of state lends itself to the straightforward calculation of phase boundaries so that complete fluid-phase equilibria can be calculated efficiently. A broad range of thermodynamic conditions of temperature and pressure are considered, and regions of vapor-liquid and liquid-liquid coexistence, including LCSTs, are found. The calculated phase boundaries at low concentrations match those measured experimentally. The temperature-composition phase diagrams of the aqueous ELP solutions at low pressure (0.1 MPa) are similar to those of types V and VI phase behavior in the classification of Scott and van Konynenburg. An analysis of the high-pressure phase behavior confirms, however, that a closed-loop liquid-liquid immiscibility region, separate from the gas-liquid envelope, is present for aqueous solutions of (VPGVG)₃₀; such a phase diagram is typical of type VI phase behavior. ELPs with shorter lengths exhibit both liquid-liquid and gas-liquid regions, both of which become less extensive as the chain length of the ELP is decreased. The strength of the hydrogen-bonding interaction is also found to affect the phase diagram of the (VPGVG)₃₀ system in that the liquid-liquid and gas-liquid regions expand as the hydrogen-bonding strength is decreased and shrink as it is increased. The LCSTs of the mixtures are seen to decrease as the ELP chain length is increased.

On the use of molecular-based thermodynamic models to assess the performance of solvents for CO2 capture processes: monoethanolamine solutions

Predictive models play an important role in the design of post-combustion processes for the capture of carbon dioxide (CO₂) emitted from power plants. A rate-based absorber model is presented to investigate the reactive capture of CO₂ using aqueous monoethanolamine (MEA) as a solvent, integrating a predictive molecular-based equation of state: SAFT-VR SW (Statistical Associating Fluid Theory-Variable Range, Square Well). A distinctive physical approach is adopted to model the chemical equilibria inherent in the process. This eliminates the need to consider reaction products explicitly and greatly reduces the amount of experimental data required to model the absorber compared to the more commonly employed chemical approaches. The predictive capabilities of the absorber model are analyzed for profiles from 10 pilot plant runs by considering two scenarios: (i) no pilot-plant data are used in the model development; (ii) only a limited set of pilot-plant data are used. Within the first scenario, the mass fraction of CO₂ in the clean gas is underestimated in all but one of the cases, indicating that a best-case performance of the solvent can be obtained with this predictive approach. Within the second scenario a single parameter is estimated based on data from a single pilot plant run to correct for the dramatic changes in the diffusivity of CO₂ in the reactive solvent. This parameter is found to be transferable for a broad range of operating conditions. A sensitivity analysis is then conducted, and the liquid viscosity and diffusivity are found to be key properties for the prediction of the composition profiles. The temperature and composition profiles are sensitive to thermodynamic properties that correspond to major sources of heat generation or dissipation. The proposed modelling framework can be used as an early assessment of solvents to aid in narrowing the search space, and can help in determining target solvents for experiments and more detailed modelling.

An accurate density functional theory for the vapor-liquid interface of associating chain molecules based on the statistical associating fluid theory for potentials of variable range

A Helmholtz free energy density functional is developed to describe the vapor-liquid interface of associating chain molecules. The functional is based on the statistical associating fluid theory with attractive potentials of variable range (SAFT-VR) for the homogenous fluid [A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, J. Chem. Phys. 106, 4168 (1997)]. A standard perturbative density functional theory (DFT) is constructed by partitioning the free energy density into a reference term (which incorporates all of the short-range interactions, and is treated locally) and an attractive perturbation (which incorporates the long-range dispersion interactions). In our previous work [F. J. Blas, E. Martin del Rio, E. de Miguel, and G. Jackson, Mol. Phys. 99, 1851 (2001); G. J. Gloor, F. J. Blas, E. Martin del Rio, E. de Miguel, and G. Jackson, Fluid Phase Equil. 194, 521 (2002)] we used a mean-field version of the theory (SAFT-HS) in which the pair correlations were neglected in the attractive term. This provides only a qualitative description of the vapor-liquid interface, due to the inadequate mean-field treatment of the vapor-liquid equilibria. Two different approaches are used to include the correlations in the attractive term: in the first, the free energy of the homogeneous fluid is partitioned such that the effect of correlations are incorporated in the local reference term; in the second, a density averaged correlation function is incorporated into the perturbative term in a similar way to that proposed by Toxvaerd [S. Toxvaerd, J. Chem. Phys. 64, 2863 (1976)]. The latter is found to provide the most accurate description of the vapor-liquid surface tension on comparison with new simulation data for a square-well fluid of variable range. The SAFT-VR DFT is used to examine the effect of molecular chain length and association on the surface tension. Different association schemes (dimerization, straight and branched chain formation, and network structures) are examined separately. The surface tension of the associating fluid is found to be bounded between the nonassociating and fully associated limits (both of which correspond to equivalent nonassociating systems). The temperature dependence of the surface tension is found to depend strongly on the balance between the strength and range of the association, and on the particular association scheme. In the case of a system with a strong but very localized association interaction, the surface tension exhibits the characteristic "s shaped" behavior with temperature observed in fluids such as water and alkanols. The various types of curves observed in real substances can be reproduced by the theory. It is very gratifying that a DFT based on SAFT-VR free energy can provide an accurate quantitative description of the surface tension of both the model and experimental systems.