Flory-Huggins equations interaction parameter

The Flory-Huggin S Interaction Parameter. These ideas, based on a study of polymer miscibility, have been applied to plasticizers according to the following equation in which V is the molar volume of the plasticizer, obtained from molar mass figures and density values at TV, and % represents the interaction parameter (11). 

A linearizing plot of the melting point depression vs. (I) theoretically starts at the origin. The Flory-Huggins-Staverman interaction parameter X, which depends principally on the temperature and the composition, can be obtained from the slope of equation (9.10). 

The Flory-Huggin s interaction parameter, x, is defined by the equation... 

Roult s law is known to fail for vapour-liquid equilibrium calculations in polymeric systems. The Flory-Huggins relationship is generally used for this purpose (for details, see mass-transfer models in Section 3.2.1). The polymer-solvent interaction parameter, xo of the Flory-Huggins equation is not known accurately for PET. Cheong and Choi used a value of 1.3 for the system PET/EG for modelling a rotating-disc reactor [113], For other polymer solvent systems, yj was found to be in the range between 0.3 and 0.5 [96],... 

Flory - a parameter in the Flory-Huggins equation to account for intermolecular interactions. X values less than 0.5 are indicative of a solvent which has relatively good solubility with a polymer. 

Equation (12-23) suffers from the same limitations as the simple solubilty parameter model, because the expression for Wm is derived by assuming that in-termolecular forces are only nondirectional van der Waals interactions. Specific interactions like ionic or hydrogen bonds arc implicitly eliminated from the model. The solubility parameter treatment described to this point cannot take such inler-actions into account because each species is assigned a solubility parameter that is independent of the nature of the other ingredients in the mixture. The x parameter, on the other hand, refers to a pair of components and can include specific interactions even if they are not explicitly mentioned in the basic Flory-Huggins theory. Solubility parameters are more convenient to use because they can be assigned a priori to the components of a mixture, x values are more realistic, but have less predictive use because they must be determined by experiments with the actual mixture. 

The comparison of the experimental solubilities [4,5] of Ar, CH4, C2H6 and CsHg in the binary aqueous mixtures of PPG-400, PEG-200 and PEG-400 with the calculated ones is presented in Figs. 1-3 and Table 2. They show that Eq. (4) coupled with the Flory-Huggins equation, in which the interaction parameter x is used as an adjustable parameter, is very accurate. The Krichevsky equation (1) does not provide accurate predictions. While less accurate than Eq. (4), the simple Eq. (2) provides very satisfactory results without involving any adjustable parameters. It should be noted that Eq. (4) coupled with the Flory-Huggins equation with X (athermal solutions) does not involve any adjustable parameters and provides results comparable to those of Eq. (2). 

Additionally, the parameters A and B are often found to depend weakly on chain lengths and composition. Shortcomings of the Flory-Huggins theory are usually lumped into the interaction parameter x- The Flory-Huggins equation (with all the corrections combined in x) contains all of the thermodynamic information needed to decide the equilibrium... 

Determination of the Flory-Huggins interaction parameter (x) for solvent-polymer pairs again requires careful fractionation of the humic macromolecules. In the view of this author, much can be learned about the ways in which humic substances are associated through determination of Flory-Huggins and solubility parameters of carefully fractionated humic substances, and through applications of empirical equations such as those of Flory-Huggins [Equation (6)] and Hildebrand-Scatchard [Equation (7)]. 

Problem 3.15 A polymer solution was cooled very slowly until phase separation took place to give two phases in equilibrium. Analysis of the phases showed that the volume fractions of polymer in the two phases were 2 = 0.01 and < 2 = 0.89, respectively. Using the Flory-Huggins equation for A/ri [cf. Eq. (3.53)], together with the equilibrium condition = A/i", calculate an estimate of the polymer-solvent interaction parameter for the conditions of phase separation. 

At Tj = 180 °C for NFBN-DPEDC and at T = 200 °C for NFBN-DCBA (isothermal polymerization), the conversions, xcp, where blends with different fractions of additive became cloudy, were measured. Figure 3 shows that the evolution of xcp with the additive fraction is weak, and xcp is always lower than the gel conversion of the cyanates, about 0.6. For a polymer blend with two components, the free energy of mixing per unit volume of blend can be expressed by the Flory-Huggins equation. Elsewhere (30), we estimate the Flory-Huggins interaction parameter x by fitting the experimental points. 

Parameter r measures the number of segments of a molecule for the term v in the Flory-Huggins equation. Parameters q, and are surface areas that are interchangeable for all except strongly hydrogen-bonded water and alcohols. Parameters r, q, and are pure-component molecular structure parameters. The combinatorial is dependent only on pure-component parameters. The residual depends additionally on binary interaction parameters and x ,... 

Between 35 and 100% R.H., the sorption isotherm is closely approximated by the Flory-Hugglns equation with an interaction parameter, x of 1.46 . 02. Since x is largely an internal energy parameter, the energy term in the Flory-Huggins equation is approximately RTx(l-<(), ), but this does not include the effect of changes in volume. The partial molar heat of sorption at constant pressure is... 

The VSM-W isotherm equation is a four parameters model, A i, K and C s). The pairwise interaction constants Aj and A j have been found to be highly correlated. To avoid this problem, Cochran et al. (1985) used the Flory-Huggin equation for the activity coefficient instead of the Wilson equation ... 

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 Flory-Huggins equation is one of the simpler models in polymer systems to accurately predict the phase behavior of a real system. In its original version with constant interaction parameters, it cannot even predict the LCST, a common phenomenon in polymer systems. However, its simple form and requirement for less number of parameters make it very suitable for more complex systems. Furthermore, parameters in the Flory-Huggins equation can be made a function of composition or even molecular weight to account for the deviation from experimental data. Thus, the Flory-Huggins model is still very useftil and one of the most frequently used methods for polymer systems. 

For PS/S/DEE systems, phase curves were measured by Wang (1997) at various temperatures and PS molecular weights. A replot of the data at 50 and 80°C at PS number average molecular weight of 25,000 g/mol is shown in Fig. 1.1.8. Note that Wang obtained tie lines that are horizontal for these systems. This means that both polymer-rich and polymer-lean phases have the same monomer composition at the same temperature. Based on the ternary Flory-Huggins equations (Eqs. 1.1.11-1.1.13), this corresponds to having the pairwise interaction parameter between S... 

In practical situations the solubility parameters of the components (also called the delta parameters 8) are used to determine whether the components are compatible or not. This solubility parameter is connected to the mutual interaction term in the Flory-Huggins equation, which equation can be written for a polymer-monomer combination as... 

Equation (5.14) represents the link between the specific retention volumes 7 , calculated from chromatographic data, and the thermodynamic interaction parameter, as defined by the Flory-Huggins approach. This parameter depends on the polymer concentration, as has been proved experimentally [12, 13]. Orofino and Flory [14] have shown that the term Xi2 92 iu eqn (5.8) represents an incomplete expression for the non-configurational contribution to the activity, this must be written as a series of powers in terms of the volume fraction, the first term being Xi2[Pg.131]

Svoboda et al. [111] used an extended form of the Flory-Huggins equation for the free-energy of mixing, in which the interaction parameter was replaced by a generalised free-energy parameter, to calculate a miscibility map for PCL/SAN... 

FH Flory-Huggins (model/equation/interaction parameter)... 

Similar expressions hold for the volatile monomers, which at high dilutions can be treated independently. At low conversions, the infinite dilution is not applicable and the multicomponent Flory-Huggins equation [Eq. (26)], for example, should be used instead. Here the y, are the volume (or segment) fractions of the various components, i = 1 up to Ny being the volatile components and the polymer being component Ny - -1 the yy, are their mole fractions, Vy the molar volumes, and the Xij the binary interaction parameters. 

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