Interaction parameter, solute-binary polymer

In the case of polymer solutions, only one component of the binary mixtures suffers firom the restrictions of chain connectivity, namely the macromolecules, whereas the solvent can spread out over the entire volume of the system. With polymer blends this limitations of chain connectivity applies to both components. In other words Polymer A can form isolated coils consisting of one macromolecule A and containing segments of many macromolecules B and vice versa. This means that we need to apply the concept of microphase equilibria twice [27] and require two intramolecular interaction parameters to characterize polymer blends, instead of the one 1 in case of polymer solutions. 

According to Flory-Huggins theory, the heat of mixing of solvent and polymer is proportional to the binary interaction parameter x in equation (3). The parameter x should be inversely proportional to absolute temperature and independent of solution composition. 

We have recently extended the Flory model to deal with nonpolar, two-solvent, one polymer soltulons (13). We considered sorption of benzene and cyclohexane by polybutadiene. As mentioned earlier, a binary Interaction parameter Is required for each pair of components In the solution. In this Instance, we required Interaction parameters to represent the Interactions benzene/cyclohexane, benzene/polybutadlene, and cyclohexane/ polybutadiene. 

The above procedure is used to predict activity coefficients of the solvents in a defined polymer solution mixture. The method yields fairly accurate predictions. Although Procedure D is a good predictive method, there is no substitute to reducing good experimental data to obtain activity coefficients. In general, higher accuracy can be obtained from empirical models when these models are used with binary interaction parameters obtained from experimental data. 

The affinity of the solute for the polymer is judged from the value of the interaction parameter. A low value of indicates greater affinity between the solute and the polymer. It is relatively very easy to measure single component, by carrying out sorption experiments and using the experimentally measured sorption data in Equations 5.11 through 5.13 as the case may be. For a binary mixture the values of x so obtained for the two components can be used to ascertain the relative sorption of the two components by the given polymer. 

The usefulness of inverse gas chromatography for determining polymer-small molecule interactions is well established (1,2). This method provides a fast and convenient way of obtaining thermodynamic data for concentrated polymer systems. However, this technique can also be used to measure polymer-polymer interaction parameters via a ternary solution approach Q). Measurements of specific retention volumes of two binary (volatile probe-polymer) and one ternary (volatile probe-polymer blend) system are sufficient to calculate xp3 > the Flory-Huggins interaction parameter, which is a measure of the thermodynamic... 

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. 

A very interesting result is the correlative and predictive performance for the UCST of binary polymer solutions with the van der Waals equation of state. Excellent correlation is achieved and reasonable prediction, using an extremely simple equation developed from athermal polymer-solvent VLE (which is simply a linear correlation of the interaction parameter with the molecular weight of the solvent). Two important comments can be made ... 

The cosolvency phenomenon was discovered in 1920 s experimentally for cellulose nitrate solution systems. Thereafter cosolvency has been observed for numerous polymer/mixed solvent systems. Polystyrene (PS) and polymethylmethacrylate (PMMA) are undoubtedly the most studied polymeric solutes in mixed solvents. Horta et al. have developed a theoretical expression to calculate a coefficient expressing quantitatively flie cosolvent power of a mixture (dTydx)o, where T,. is the critical temperature of the system and x is the mole fraction of hquid 2 in the solvent mixture, and subscript zero means x—>0. This derivative expresses the initial slope of the critical line as a function of solvent composition (Figure 5.4.1). Large negative values of (dT/dx) are the characteristic feature of the powerful cosolvent systems reported. The theoretical expression developed for (dT dx)o has been written in terms of the interaction parameters for the binary systems ... 

Where Xij is the binary interaction parameter between gases i and j. For simplicity this model assumes no higher interaction parameters between the gases and polymer, e.g. Xkbc = 0. Again, Equation (11.21) can be simplified by the same assumptions used in the binary and tertiary systems. The solution, assuming gases B and C obey Henry s law, is ... 

The scattered intensity of light due to concentration flucmations, extrapolated to zero-scattering angle, is inversely proportional to the second derivative of AG . Thus, it can be used to determine the location of a spinodal, i.e., the spinodal temperature, T for the given mixmre. As Eq. 2.32 indicates, LS makes it possible to determine also the second virial coefficient (A2) and from it the binary interaction parameter ix )- However, this technique is applicable only to homogenous systems, i.e., at temperatures T for those having UCST. As mentioned in Sect. 2.S.2.2, the LS methods has been used primarily to study the phase equilibria of polymer solutions. 

The binary interactirMi generally refers to the interactions between polymer-polymer and polymer-solvent The nature of solvent-polymer interaction plays an important role in the miscibility of blends. Many thermodynamic properties of polymer solutions such as solubility, swelling behavior, etc., depend on the polymer-solvent interaction parameter (y). The quantity was introduced by Flory and Huggins. Discussions of polymer miscibility usually start with Flory-Huggins equation for free energy of mixing of a blend (refer to Chap. 2, Thermodynamics of Polymer Blends ). 

The introduction of a relevant expression for the critical determinant in the mean-field lattice gas model for binary systems is discussed here. It leads to an alternative and thermodynamic consistent method of adjusting two-particle interaction functions to experimental critical binary 1iquid-vapour densities. The present approach might lead to new developments in the determination of MFLG parameters for the mixture in small-molecule mixtures and in polymer solutions and polymer mixtures (blends). These relevant critical conditions appear because of the extra constraint, which is the equation of state, put on the hole model, and are... 

This is a simple model and cannot account for all the issues of mixture thermodynamics. Interaction parameters deduced from various phase behavior information are often believed to include other effects than purely enthalpic ones. This way, the LCST (lower critical solution temperature) behavior observed in polymer blends can be explained and accounted for quantitatively. These theories refine the binary interaction parameter by removing extraneous effects. EOS effects do not favor phase... 

Once the binary interaction parameters for the blend system are known, EOS theory can be used to predict phase separation behavior. Lower critical solution temperature (LCST) is the temperature above which a miscible system becomes immiscible. Upper critical solution temperature (UCST) is the temperature above which an immiscible polymer blend system becomes miscible. Some polymer-polymer systems exhibit either LCST or UCST or both or neither. Another set of phase separation can be obtained as shown in the copolymer-homopolymer example in Section 3.2 by varying the blend volume fraction. The Gibbs free energy of mixing per unit volume for a binary system of two polymers can be written as... 

The FH model for the activity coefficient, proposed in the early 1940s by Flory and Huggins, is a famous Gibbs free energy expression for polymer solutions. For binary solvent-polymer solutions and assuming that the parameter of the model, the so-called FH interaction parameter x,2, is constant, the activity coefficient is given by the equation ... 

Introducing fillers in the melt of a binary polymer mixture leads to the following consequences. The main effect is a selective adsorption of one of the components at the interface with the solid. Above the critical point in the phase diagram (for the systems with UCST) polymer melt is a solution of one component into another. The thermodynamic interaction parameter Xab depends on temperature and melt composition. The interaction of each component with the surface is characterized by the thermodynamic parameter of interaction between one of the components and the surface, Xsa or Xsb-In such a system, selective adsorption proceeds, depending on the relation between Xsa tid Xsb- The selectivity of the interaction of the polymer mixture components with the solid plays an important role in the thermodynamic behavior of a filled polymer melt. Let us consider some simple thermodynamic... 

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