Interaction parameter, solute-binary polymer mixture

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... 

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... 

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. 

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 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 ... 

It is well known that electrical conductivity of liquid solutions depends on the concentration of ions and their activity. The aqueous fluids in pipelines usually are electrolyte solutions and the conductivity is proportional to the salt concentration. The activity of the ions is related to temperature, and impurity like nonconductive chemical additives. Measurements of electrical conductivity could directly reflect the concentrations of chemicals such as salts, THIs (alcohol) and KHIs (polymers). (Clay and Medwin, 1977) [6] presented a simple correlation in which the sound velocity in sea water was described as a function of sahnity and temperature. Acoustic velocity has been successfully applied to investigate a variety of solutions and binary gas mixtures (Jerie, et al., 2004 Vibhu, et al., 2004 Goodenough, et al., 2005 Vyas, et al., 2006) [11] [25] [9] [26]. As a result, electrical conductivity and acoustic velocity were chosen as two parameters to simultaneously determine both salt and inhibitor concentrations. Artificial neural network (ANN) provides a numerical tool for such applications in which multi-parameter correlations are needed but the interaction and the relations between the parameters are not well known (Sundgren, et al., 1991 Broten and Wood, 1993) [21] [4]. Therefore, ANN correlations were developed to determine salt and inhibitor concentrations using the measured electrical conductivity, acoustic velocity, and temperature. 

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... 

Despite the fact that these solutions represent binary systems, at least three Hory-Huggins interaction parameters are involved in their modeling, like with ternary mixtures. Because of the necessity to account for the interaction of the solvent with monomer A and with monomer B, plus the interaction between the polymers A and B, one should expect the need for a minimum of two additional parameters. Experimental data obtained for solutions of a given copolymer of the type A-ran-B with a constant fraction / of B monomers can be modeled [25] by means of (32), with one set of a, v, and parameters. For predictive purposes, it would of course be interesting to find out how these parameters for the copolymer solution (subscripts AB) relate to the parameters for the solutions of the corresponding homopolymers in the same solvent (subscripts A and B, respectively) at the same temperature. 

This intricate scheme of interaction may be described in terms of sets of compatibility parameters easily calculated (or measured) for relevant binary systems (e.g., side chain/solvent, core/solvent, core/side chain) [49,50]. The knowledge of pairwise parameters is also necessary for a quantitative assessment of the temperature variation of solubility and demixing (two liquid phases or crystallization). According to an approximate treatment of binary solutions originally developed for mixtures of poorly interacting apolar polymers, a liquid-liquid phase separation is expected to occiu at a critical temperature T = 0 > 0 at which a balance of the enthalpy (k) and entropy i/r) components... 

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