Polymer solubility, thermodynamic models

CHEOPS is based on the method of atomic constants, which uses atom contributions and an anharmonic oscillator model. Unlike other similar programs, this allows the prediction of polymer network and copolymer properties. A list of 39 properties could be computed. These include permeability, solubility, thermodynamic, microscopic, physical and optical properties. It also predicts the temperature dependence of some of the properties. The program supports common organic functionality as well as halides. As, B, P, Pb, S, Si, and Sn. Files can be saved with individual structures or a database of structures. 

Thermodynamic modelling of solution phases lies at the core of the CALPHAD method. Only rarely do calculations involve purely stoichiometric compounds. The calculation of a complex system which may have literally 100 different stoichiometric substances usually has a phase such as the gas which is a mixture of many components, and in a complex metallic system with 10 or 11 alloying elements it is not unusual for all of the phases to involve solubility of the various elements. Solution phases will be defined here as any phase in which there is solubility of more than one component and within this chapter are broken down to four types (1) random substitutional, (2) sublattice, (3) ionic and (4) aqueous. Others types of solution phase, such as exist in polymers or complex organic systems, can also be modelled, but these four represent the major types which are currently available in CALPHAD software programmes. 

The solubility of hydrocarbons in rubbery polymers can be described in more detail by several theories of solutions using various criteria of thermodynamic affinity [7,25-28], of which the Flory-Huggins theory is the most popular one. It takes into account the volume content of the penetrant dissolved in the polymer and the change in the length of the polymer s thermodynamic segment as a result of dissolution [7]. However, it should be pointed out that to describe dissolution, a rehned dual-mode sorption model can be used, e.g., the model by Pace and Datyner [7,29,30]. 

THERMODYNAMIC MODELS OF POLYMER SOLUBILITY AND PHASE SEPARATION... 

Section 16.2 will discuss the concept and importance of the group-contribution (GC) approach in estimating two polymer properties, which are relevant for polymer solutions and blends the density and the solubility parameter. The GC technique is employed in several of the thermodynamic models discussed later in the chapter. 

Many properties of pure polymers (and of polymer solutions) can be estimated with group contributions (GC). Examples of properties for which (GC) methods have been developed are the density, the solubility parameter, the melting and glass transition temperatures, as well as the surface tension. Phase equilibria for polymer solutions and blends can also be estimated with GC methods, as we discuss in Section 16.4 and 16.5. Here we review the GC principle, and in the following sections we discuss estimation methods for the density and the solubility parameter. These two properties are relevant for many thermodynamic models used for polymers, e.g., the Hansen and Flory-Hug-gins models discussed in Section 16.3 and the free-volume activity coefficient models discussed in Section 16.4. 

The solubility parameter is a very important property in science and has found widespread use in many fields and not just in the smdy of polymer-solvent thermodynamics. It is connected to the Flory-Huggins model as well, as explained in Section 16.3.3.2, but can also be used independent of it, as discussed in Sections 16.3.3.1 and 16.3.3.3. Several handbooks and reference books provide extensive lists of solubility parameters of numerous chemicals.The solubility parameter is defined as... 

The Hansen method is very valnable. It has fonnd widespread use particularly in the paints and coatings indnstry, where the choice of solvents to meet economical, ecological, and safety constraints is of critical importance. It can explain cases in which polymer and solvent solubility parameters are almost perfectly matched, yet the polymer will not dissolve. The Hansen method can also predict cases where two nonsolvents can be mixed to form a solvent. Still, the method is approximate, it lacks the generality of a Ml thermodynamic model for assessing miscibility, and it requires some experimental measnrements. The determination of R is typically based on visnal observation of solubility (or not) of 0.5 g polymer in 5 cm solvent at room temperature. Given the concentration and the temperature dependence of phase boundaries, such a determination may seem a bit arbitrary. Still the method works out pretty well in practice, probably because the liquid-liquid boundaries for most polymer-solvent systems are fairly flat. ... 

Also a thermodynamic model based on the coupled Equation of State model and Flory-Huggins theory for polymer solutions was developed. The model parameters such as solubility-parameter of asphaltenes, molecular weight of asphaltenes, and molar volume of asphaltenes were obtained by fitting the model to experimental data. 

A thermodynamic model based on Flory-Huggins polymer-solution theory was developed and coupled with Equation of State model to predict the amount of asphaltene precipitation. The model prediction shows close agreement with the experimental data after regression of asphaltene properties such as molar volume, solubility parameter and molecular weight. The model, however, fails to account for the effect of large changes in the solubility parameters of the oil-solvent mixtures. 

This chapter summarizes the thermodynamics of multicomponent polymer systems, with special emphasis on polymer blends and mixtures. After a brief introduction of the relevant thermodynamic principles - laws of thermodynamics, definitions, and interrelations of thermodynamic variables and potentials - selected theories of liquid and polymer mixtures are provided Specifically, both lattice theories (such as the Hory-Huggins model. Equation of State theories, and the gas-lattice models) and ojf-lattice theories (such as the strong interaction model, heat of mixing approaches, and solubility parameter models) are discussed and compared. Model parameters are also tabulated for the each theory for common or representative polymer blends. In the second half of this chapter, the thermodynamics of phase separation are discussed, and experimental methods - for determining phase diagrams or for quantifying the theoretical model parameters - are mentioned. 

The Flory—Huggins theory, which is based upon statistical thermodynamic models, has been used to assess the miscibility of polymer blends and was developed by Flory (1941, 1942) and Huggins (1941,1942) in the 1940s. Unlike the Hildebrand solubility parameter, it provides a fundamental understanding backed with classical thermodynamic theories. 

Predictive models for drug-polymer miscibility have been introduced, and they are largely derived from solution thermodynamics. Lattice-based solution models, such as the F-H theory, can be used to assess miscibility in drug-polymer blends, for which the F-H interaction parameter can be considered as a measure of miscibility. In addition, solubility parameter models can be used for this purpose. The methods used to estimate interaction parameters include melting point depression and the determination of solubility parameters using group contribution theory. 

Amorphous material has higher apparent solubility and can remain in supersaturated state upon transit from gastric compartment to the intestinal compartment with or without the assistance of precipitation inhibitors. According to the model of API in polymer solubility (Marsac et al. 2006b), APIs have the tendency to crystallize to the more thermodynamically stable form. Inhibition of API crystallization in solid dispersion is attributed predominantly to kinetic stabilization (Marsac et al. 2006b). 

Using standard thermodynamics and Equation 3.8, it can be shown that for high molecular weight polymer-solvent systems, the polymer critical concentration is close to zero and the interaction parameter has a value equal to 0.5. Thus, a good solvent (polymer soluble in the solvent at all proportions) is obtained if Xu 0-5, while values greater than 0.5 indicate poor miscibility. Since the FH model is only an approximate representation of the physical picture and particularly the FH parameter is often not a constant at all, this empirical rule is certainly subject to some uncertainty. Nevertheless, it has found widespread use and its conclusions are often in good agreement with experiment. 

Turbidity measurements use the onset of two-phase separation when adding a non-solvent to a dilute polymer solution in a good solvent. Two different non-solvents have to be used one having a solubility parameter above that of the (good) solvent, and another having a solubility parameter below that of the solvent. A series of experiments has to be done to find the solvent-polymer pair with 62 = di. Liquid-liquid equilibrium (LLE) curves of binary polymer solutions ean also be applied for the determination of solubility parameters of polymers. An appropriate thermodynamic model relating cloud-point or coexistence data with Xh is necessary, however. 

Keywords Copolymers Equation of state Modeling Polymers Solubility Sorption Thermodynamics... 

However, experimental data on polymer solubility are often scarce. Considerable experimental effort is generally required for determining these properties of polymer systems. Thermodynamics can provide powerful and robust tools for modeling of experimental data and even for prediction of the thermodynamic behavior. 

Polymers are often polydisperse with respect to molecular weight. Whereas this is of minor importance for the solvent sorption in polymers (vapor-hquid equilibrium), this fact usually remarkably influences the polymer solubility (liquid-hquid equilibrium). Therefore, polydispersity needs to be accounted for in interpretation and modeling of experimental data. This can be done by applying continuous thermodynamics as well as by choosing a representative set of pseudocomponents. It was shown that a meaningful estimation of the phase boundary is possible when using only two or three pseudocomponents as soon as they reflect the important moments (Mn, Mw, Mz) of the molecular weight distribution. 

A thermodynamic model was recently proposed to calculate the solubility of small molecules in assy polymers. This model is based on the assumption that the densiQr of the polymer matrix can be considered as a proper order parameter for the nonequilibrium state of the system (7). In this chapter, the fundamental principles of the model are reviewed and the relation of the model to the rheological properties of the polymeric matrix is developed. In particular, a unique relation between the equilibrium and non-equilibrium properties of the polymer-penetrant mixture can be obtained on the basis of a simple model for the stress-strain relationship. 

In conclusion, it can be said that the partitioning behaviour of monomers between the different phases present during an emulsion polymerisation can be described and predicted using a simple thermodynamic model derived from the classical Flory-Huggins theory for polymer solutions. In general, therefore, the monomer concentrations at the locus of polymerisation are relatively easily accessible. However, this is not the case for more water-soluble monomers (acrylic acid etc). For these monomers suitable models are not readily available and one has to rely on the experimental data. 

The development of a thermodynamic model for the multi-conponent polymer/gas system is one way to investigate the solubility of gas mixtures in a polymer. In this paper, the solubihty of a gas mixture in a polymer melt is measmed with a magnetic suspension balance (MSB). Using methods similar to those used for the single-gas/single-polymer system, a thermodynamic model for the multi-conponent system was derived. The Simha-Somcynsky (SS) equation of state (EOS) [26-29] was used as an example to derive the thermodynamic model. 

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