Statistical thermodynamics of associated polymer solutions (original) (raw)
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Statistical Thermodynamics of Polymer Solutions
Macromolecules, 1978
The lattice fluid theory of solutions is used to calculate heats and volumes of mixing, lower critical solution temperatures, and the enthalpic and entropic components of the chemical potential. Results of these calculations are compared with literature data on several polyisobutylene solutions. In most instances the agreement with experiment is favorable and comparable to that obtained with the Flory equation of state theory. Several insights into polymer solution behavior are obtained and include: (1) differences in equation of state properties of the pure components make an unfavorable entropic contribution to the chemical potential that becomes large and dominant as the gas-liquid critical temperature of the solvent is approached; (2) limited miscibility of nonpolar polymer solutions at low and high temperatures is a manifestation of a polymer solution's small combinatorial entropy; and (3) negative heats of mixing in nonpolar polymer solutions are caused by the solvent's tendency to contract when polymer is added. Suggestions on how the theory can be improved are made Freeman and Rowlinson' in 1960 observed that several hydrocarbon polymers dissolved in hydrocarbon solvents phase separated at high temperatures. These nonpolar polymer solutions exhibited what are known as lower critical solution temperatures (LCST), a critical point phenomenon that is relatively rare among low molecular weight solutions. Soon after the discovery of the universality of LCST behavior in polymer solutions, Flory and c o -~o r k e r s~-~ developed a new theory of solutions which incorporated the "equation of state" properties of the pure components. This new theory of solutions, hereafter referred to as the Flory theory, demonstrated that mixture thermodynamic properties depend on the thermodynamic properties of the pure components and that LCST behavior is related to the dissimilarity of the equation of state of properties of polymer and solvent. P a t t e r~o d -~ has also shown that LCST behavior is associated with differences in polymer/solvent properties by using the general corresponding states theory of Prigogine and collaborators.1° Classical polymer solution theory, i.e., Flory-Huggins theory," which ignores the equation of state properties of the pure components, completely fails to describe the LCST behavior.
Macromolecular Theory and Simulations, 1994
The Gibbs free energies and equations of state of polymers with special molar mass distributions, e. g., Flory distribution, uniform distribution and Schulz distribution, are derived based on a lattice fluid model. The influence of the polydispersity (or the chain length) on the close-packed mass density, the close-packed volume of a mer and the mer-mer interaction energy or the scaling temperature is discussed. The diagrams of the Gibbs free energies as a function of temperature and chain length are simulated with a computer. The results suggest that a polydisperse polymer is thermodynamically more stable than the corresponding monodisperse polymer and that the thermodynamical properties of a polydisperse polymer are identical with those of the corresponding monodisperse polymer when the average degree of polymerization is sufficiently high.
Macromolecular Chemistry and Physics, 2003
A simple expression for the composition dependence of the Flory-Huggins interaction parameter of polymer/solvent systems reported earlier is used to model the demixing of polymer solutions into two liquid phases. To this end the system specific parameters ζ and ν of that approach are calculated as a function of temperature using the thermodynamic expressions resulting for the critical conditions on one side and from experime ntally determined critical data for polymers of different molar mass on the other side. By means of data reported for the system cyclohexane/polystyrene it is demonstrated that binodal and spinodal lines are very accurately modeled at low temperatures (UCSTs) and at high temperatures (LCSTs). The parameters obtained from the demixing behavior match well with that calculated from the composition dependence of the vapor pressure at temperatures where the components are completely miscible. Information on the phase separation of the system transdecalin/polystyrene for different molecular weights and at different elevated pressures is used to show that the approach is also apt to model pressure influences. The thus obtained ζ (T;p) and ν (T;p) enable the prediction of the (endothermal) theta temperature of the system as a function of pressure in quantitative agreement with the data directly obtained from light scattering measurements with dilute solutions.
Journal of Polymer …, 2002
We extend to ternary solutions our previous study of conformational, thermodynamic, and rheological properties of semidilute polymer solutions in good solvent. Osmotic pressure and viscosity measurements were performed in several mixtures of two compatible polymers in a common solvent. Renormalization group results were used to analyze the data, using de Gennes's blobs model to connect dynamic and conformational properties.
Thermodynamics of polymer solutions as functions of pressure and temperature
Journal of Colloid and Interface Science, 1972
The construction of a light scattering photometer for use at different temperatures and pressures up to 1000 atm permits measurement of the chemical potential and the second osmotic virial coefficient for high polymer solutions. From this one can determine entropy, enthalpy, and volume changes of solvent on dilution. Measurement of the scattered intensity at several wavelengths (the scattering angle being held constant) gives the dimensions of the dissolved molecules. The above-mentioned quantities are determined for polystyrene and polyisobutylene in different solvents as functions of pressure, temperature and molecular weight. The total number of experiments shows the following results: 1. The enthalpies of dilution are shifted in the same direction with increasing pressure. All endothermal systems become more endothermal with increasing pressure and all exothermal ones become less exothermal. Both for endothermal and exothermal pseudoideal systems the appropriate ~ temperatures (A2 = 0) increase with growing pressure. 2. Calculation of volume changes of solvent on dilution (by measuring the pressure dependence of light scattering) shows that these volume changes are positive for endothermal systems and negative for athermal and exothermal ones. A theoretical treatment is made on the basis of the excluded volume theory and the principle of corresponding states.
Journal of Applied Polymer Science, 2009
In this study, the recently proposed model by Pazuki et al., based on the local composition concept (LCC), has been used in correlating the vapor-liquid phase behavior of polymer solutions. Similar to the LCC models available in the literature, the proposed model has two combinatorial and residual terms to account for both entropic as well as enthalpic effects in solution. The Flory-Huggins model has been considered as the combinatorial part of the proposed model, while the equation proposed by Pazuki et al. was considered as the residual term. The proposed model has been used in correlating the vapor-liquid phase behavior for a large number of polymer-solvent mixtures at different conditions. The results obtained from the proposed model have been compared with those obtained from the UNIQUAC-FV model. The results showed that the pro-posed model can accurately correlate the VLE data for polymer solutions studied in this work. Also, the proposed model has been used to obtain the thermophysical properties such as density, viscosity, and excess enthalpy for these polymer solutions. The results in connection with the thermophysical properties obtained from the proposed model have been compared with those obtained from the Poly-NRTL and the Poly-Wilson models. The results showed that the proposed model can accurately correlate the properties of polymer solutions at various conditions.
Fluid Phase Equilibria, 2006
Copolymers are increasing their importance from the commercial point of view, mainly due to their tuned physical properties for specific applications in the polymer manufacturing. Copolymers allow tailoring new materials with desirable features by blending specific copolymers, which contribute for the physical properties of the final material. The description of the fluid-phase equilibrium of copolymer + solvent mixtures by thermodynamic models is essential for the design of new manufacture processes. In this work, vapor-liquid equilibrium data for several copolymer + solvent mixtures were modeled using two theoretical equations of state: one based on the lattice gas theory (LGT) and another one based on the statistical association fluid theory, called perturbed chain-SAFT (PC-SAFT). The results show that the PC-SAFT equation of state provides a better representation of the experimental data in terms of pressure deviations.