POLYMER SOLUTIONS AND BLENDS

FIGURE 11-2 Two gases separated by a barrier (top) and after removal of the barrier (bottom). What you do not see is the constant random motion of the gas molecules. 

Calculating the entropy change in the surroundings would be hard, but because this entropy change is a consequence of an exchange of heat with the system, we can then write Equation 11-3 (assuming the process is reversible)  

We can now define the free energy for a constant pressure process (i.e., the Gibbs free energy) to be Equation 11-5  

FIGURE 11-3 Schematic diagram of the mixing of polymer in solvent 

The enthalpy and entropy of mixing in the equation for the free energy (Equation 11-6)  

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In polymer solutions and blends, it becomes of interest to understand how the surface tension depends on the molecular weight (or number of repeat units, IV) of the macromolecule and on the polymer-solvent interactions through the interaction parameter, x- In terms of a Hory lattice model, x is given by the polymer and solvent interactions through... 

Interestingly, dynamic equations of the same form have recently been set up for polymer solutions and blends except for the difference in the expression of the elastic stress [76]. We will discuss this aspect in the following section. 

Harris,E.K, Jr. Viscometric properties of polymer solutions and blends as functions of concentration and molecular weight. Ph. D. thesis, University of Wisconsin, 1970. 

Window autoclaves have been built to allow one to determine visually the appearance of turbidity in a homogeneous polymer solution, indicating the onset of phase separation, and to observe the resulting number of liquid and gaseous phases and optionally to determine their composition. Lentz [40] developed a mechanically driven stirrer fitted in a 2000-bar window autoclave. This apparatus allowed fast homogenation of concentrated polymer solutions and blends having low viscosity. 

Before discussing theoretical approaches let us review some experimental results on the influence of flow on the phase behavior of polymer solutions and blends. Pioneering work on shear-induced phase changes in polymer solutions was carried out by Silberberg and Kuhn [108] on a polymer mixture of polystyrene (PS) and ethyl cellulose dissolved in benzene a system which displays UCST behavior. They observed shear-dependent depressions of the critical point of as much as 13 K under steady-state shear at rates up to 270 s Similar results on shear-induced homogenization were reported on a 50/50 blend solution of PS and poly(butadiene) (PB) with dioctyl phthalate (DOP) as a solvent under steady-state Couette flow [109, 110], A semi-dilute solution of the mixture containing 3 wt% of total polymer was prepared. The quiescent... 

In the following sections, examples of SANS investigations from polymer systems are considered. Simple cases involving polymer solutions and blends are described in order to demonstrate the modeling approaches discussed here. These examples have been borrowed from my recent work in collaboration with other scientists at the National Institute of Standards and Technology. 

Qian, C. Mumby, S.J. Eichinger, B.E., "Phase Diagrams of Binary Polymer Solutions and Blends," Macromolecules, 24, 1655 (1991). 

Now we turn our attention to the phase behavior of polymer solutions and blends and the questions we asked right at the beginning of this chapter will a particular polymer dissolve in a given solvent or mix with another chosen polymer ... 

We begin by reviewing apphcations of the proposed HPTMC method to polymer solutions and blends. For pure polymer solutions, we simulate chains consisting of up to 16,000 sites for simple-cubic lattice models and 500 sites... 

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. 

These three approaches have found widespread application to a large variety of systems and equilibria types ranging from vapor-liquid equilibria for binary and multicomponent polymer solutions, blends, and copolymers, liquid-liquid equilibria for polymer solutions and blends, solid-liquid-liquid equilibria, and solubility of gases in polymers, to mention only a few. In some cases, the results are purely predictive in others interaction parameters are required and the models are capable of correlating (describing) the experimental information. In Section 16.7, we attempt to summarize and comparatively discuss the performance of these three approaches. We attempt there, for reasons of completion, to discuss the performance of a few other (mostly) predictive models such as the group-contribution lattice fluid and the group-contribution Flory equations of state, which are not extensively discussed separately. 

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. 

Equations of state offer a number of advantages over activity coefficient models for example, they can be applied to both low and high pressures, for properties other than phase equilibria, and the density is not required as an input parameter. However, often they are more difficult to develop for complex fluids and mixtures than are activity coefficient models. Very many equations of state have been proposed for polymers Section 16.7 discusses the reason. Recent reviews have been presented. " " We will not attempt to cover all the various approaches, but essentially discuss in detail only two of them, which seem promising for polymer solutions and blends the cubic equations of state and the SAFT (Statistical Associating Fluid Theory) method. 

The various cubic equations of state have been quite extensively applied to polymer solutions and blends since 1990. More specifically ... 

Why have so many different models been developed for polymer systems The simation could be easily considered confusing for the practicing engineer. Polymer solutions and blends are complicated systems the frequent occurrence of LLE in many forms (UCST, LCST, closed loop), the significant effect of temperature and polymer molecular weight in phase equilibria, the FV effects, and other factors cause these difficulties. The choice of a suitable model depends on the actual problem and demands, especially the following ... 

Simple cubic equations of state can correlate both VLE and LLE for polymer solutions and blends with a single interaction parameters. They can be combined with an activity coefficient model for predictive calculations using the so-called EoS/G mixing rules. Applications of cubic equations of state to high pressures are so far limited to those shown for the Sako et al. cubic equation of state. 

On the other hand, Doi and Onuki (Doi and Onuki 1992) proposed both a dynamic structure factor S(q,t) and a time-dependent modulus G(t), considering the dynamic coupling between stress and composition in polymer solutions and blends ... 

Xie, H. K., Nies, E., Stroeks, A., and Simha, R., Some considerations on equation of state and phase-relations polymer-solutions and blends, Polym. Eng. ScL, 32,1654—1664 (1992). 

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