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Flory equation of state

The Flory equation of state does not reduce to the ideal gas equation of state at zero pressure and infinite volume. Flory and his coworkers derived the equation of state specifically for liquid polymer solutions and were not concerned with the performance of the equation in the vapor phase. Poor vapor phase performance of an equation of state causes considerable difficulty, however, when one tries to apply the equation to higher pressure, higher temperature situations. The Chen et al. equation of state was developed in order to remedy this deficiency of the Flory equation of state. [Pg.17]


Bogdanic, G., Fredenslund, A. Revision of the Group-Contribution Flory Equation of State for Phase Equilibria Calculations in Mixtures with Polymers. 1. Prediction of Vapor-Liquid Equilibria for Polymer Solutions. Ind. Eng. Chem. Res. 1994,33 1331-1340. [Pg.122]

The Oishi-Prausnitz model cannot be defined strictly as a lattice model. The combinatorial and residual terms in the original UNIFAC and UNIQUAC models can be derived from lattice statistics arguments similar to those used in deriving the other models discussed in this section. On the other hand, the free volume contribution to the Oishi-Prausnitz model is derived from the Flory equation of state discussed in the next section. Thus, the Oishi-Prausnitz model is a hybrid of the lattice-fluid and free volume approaches. [Pg.16]

Holten-Andersen et al. (1987) modified the Flory equation of state in order to develop an equation that is applicable to the vapor phase, to make it more applicable to associating fluids, and to introduce a group contribution approach. Chen et al. (1990) revised and improved the equation of state. The final model takes the following form. [Pg.18]

The procedure is based on the group contribution equation of state by F. Chen, Aa. Fredenslund, and P. Rasmussen, "A Group-Contribution Flory Equation of State for Vapor-Liquid Equilibria" Ind. Engr. Chem. Res., 29, 875 (1990). [Pg.69]

Unusual Properties of PDMS. Some of the unusual physical properties exhibited by PDMS are summarized in List I. Atypically low values are exhibited for the characteristic pressure (a corrected internal pressure, which is much used in the study of liquids) (37), the bulk viscosity i, and the temperature coeflScient of y (4). Also, entropies of dilution and excess volumes on mixing PDMS with solvents are much lower than can be accounted for by the Flory equation of state theory (37). Finally, as has already been mentioned, PDMS has a surprisingly high permeability. [Pg.55]

Polymer blends typically show a decrease in miscibility with increasing temperature. [27] McMaster has used a modified Flory equation of state thermodynamic model to show that the existence of a lower critical solution temperature (LCST) is caused mainly by differences in the pure component thermal expansion coefficients. [Pg.27]

The liquid may be a good or poor solvent for the polymer. For this type of system a theoretical relation can be obtained for K by applying the Flory equation of state theory ( -i) or lattice fluid theory (7-10) of solutions. An important prerequisite for the application of these theories is for the polymer to behave as an equlibrium liquid. This condition is generally valid for a lightly crosslinked, amorphous polymer above its Tg or for the amorphous component of a semi-crystalline polymer above its Tg. [Pg.171]

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. [Pg.684]

The combinatorial and residual terms are obtained from the original UNIFAC. An additional term is added for the FV effects. An approximation but at the same time an interesting feature of UNIFAC-FV and the other models of this type is that the same UNIFAC group-interaction parameters, i.e., those of original UNIFAC, are used. No parameter estimation is performed. The FV term used in UNIFAC-FV has a theoretical origin and is based on the Flory equation of state ... [Pg.707]

FIGURE 16.6 Molecular structure of the paint Araldit 488 and infinite dilution activity coefficients (Qf) with various models for Araldit 488-solvent systems. Results are shown with the Entropic-FV and UNIFAC-FV activity coefficient models and the GC-Flory equation of state. The calculations with the two activity coefficient models are shown for two different values of the density of the polymer, predicted by the GC-VOL and van Krevelen models. (Modified from Lindvig et al., AIChE J., 47(11), 2573-2584, 2001.)... [Pg.713]

FIGURE 16.7 Average deviations in solid-liquid equilibrium calculations, as a function of the solute carbon number, for alkane systems using various FV models. E-FV is the Entropic-FV model. F-FVl.l is the Flory-FV model using c= 1.1. GCFLORY EoS is the GC-Flory equation of state. (From Coutinho, J.A.P. et al.. Fluid Phase Equilibria, 103, 23, 1995. With permission.)... [Pg.715]

Dee applied the Flory equation of state to PS/cyclohexane/water, but the results are only of correlative value. [Pg.734]

Table I. Pure Component and Mixture Properties for Flory Equation of State Thermodynamics (10)... Table I. Pure Component and Mixture Properties for Flory Equation of State Thermodynamics (10)...
The scale of phase separation can also be estimated using the Flory equation of state thermodynamics (see Ref. 10 for details of the analytic expressions for d2f/d2 and xilO With appropriate expressions for d2f/d2 and Xi2> Equation 10 can be substituted into Equation 7 and evaluated numerically. Some typical values for sets of parameters originally used by McMaster are shown in Figure 2. For all cases considered, the scale of phase separation is somewhat larger than the Flory-Huggins value (with xi2. = 0). In no case was the scale of phase separation more than ca. 2.5 times the Flory-Huggins scale. Similar results are obtained if non-zero values of X12. are used in Equation 11. Hence, Equation 12 provides a reasonable lower bound on the scale of phase separation. [Pg.65]

Roe and Zin analyzed the value of the polymer-polymer interaction energy density and its temperature dependence obtained in their work. Starting from the Flory equation-of-state theory they derived the following expression for A ... [Pg.558]

In the Flory equation of state theory [12, 16—21] the parameter of interaction between the volatile substance and the binary stationary phase is written as [26] ... [Pg.134]

In response to the developing field of polymer blends, two new theories of polymer mixing were developed. The first was the Flory equation of state theory (19,20), and the second was Sanchez s lattice fluid theory (21 4). These theories were expressed in terms of the reduced temperature, T = TIT, ... [Pg.153]

The free-volume and residual terms are calculated from a modification of the original Flory equation of state, Eq. (55), where v is the reduced volume, defined by Eq. (56). [Pg.36]

High-pressure phase equilibria in systems of polymers, solvents, and supercritical gases are in almost all cases modeled using equations of state. A review of equations of state for polymer systems, including a discussion of their theoretical background, has been given by Lambert et al. [6]. One of the first equations of state that was used to model the high-pressure phase behavior of polymer-solvent systems was the Flory equation of state [11, 12]. Patterson and Delmas [10] showed that this equation of state can be used to describe both LCST and UCST phase behavior. The perturbed hard-chain theory (PCHT) was developed by Prausnitz and coworkers [57-59]. It can be considered as an improvement of the approach of Flory... [Pg.39]

Wichert, J. M. Gulati, H. S. Hall, C. K. J. (1996). Binary hard chain mixtures. I. Generalized Flory equations of state. /. Chem. Phys., Vol. 105, 7669-7682 Woodward, C. E. Forsman, J. (2008). Density functional theory for polymer fluids with molecular weight polydispersity. Phys. Rev. Lett., Vol. 100,098301 Woodward, C. E. (1991). A density functional theory for polymers Application to hard chain-hard sphere mixtures in slitlike pores. /. Chem. Phys., Vol. 94,3183-3191 Woodward, C. E. Forsman, J. (2009). Interactions between surfaces in polydisperse semiflexible polymer solutions. MacromoL, Vol. 42, 7563-7570 Woodward, C. E. Yethiraj A. (1994). Density functional theory for inhomogeneous polymer solutions. /, Chem. Phys., Vol. 100,3181-3186... [Pg.150]

The Flory equation of state approach has been shown to be quite applicable to polymer mixtiues (see McMaster [ 14]). The Flory equation of state approach involved the characterization of components by three parameters v (the characteristic volume), T (the characteristic temperatiue) and P (the characteristic pressure). Reduced variables are defined as ... [Pg.19]

Fig. 1.12 Osmotic pressure JlV/k T plotted vs. volume fraction 4>, for the athermal bond fluctuation model on the simple cubic lattice, N = 20. Open squares are obtained by Deutsch and Dickman with the repulsive wall method full squares are based on thermodynamic integration over a variable excluded volume interaction between the inserted ghost chain and the other chains. Curve shows the pressure according to the Generalized Flory equation of state of Ref. 172, H , )lkiT- < >], where v N) is the exclusion volume of an iV-mer. (From Muller and Paul. )... Fig. 1.12 Osmotic pressure JlV/k T plotted vs. volume fraction 4>, for the athermal bond fluctuation model on the simple cubic lattice, N = 20. Open squares are obtained by Deutsch and Dickman with the repulsive wall method full squares are based on thermodynamic integration over a variable excluded volume interaction between the inserted ghost chain and the other chains. Curve shows the pressure according to the Generalized Flory equation of state of Ref. 172, H <j),N)/k T = . <p/N + lki[v N)lv( )m (j>, )lkiT- < >], where v N) is the exclusion volume of an iV-mer. (From Muller and Paul. )...
T, P, and v can be determined from the Flory equation of state theory. [Pg.178]


See other pages where Flory equation of state is mentioned: [Pg.588]    [Pg.589]    [Pg.4]    [Pg.15]    [Pg.18]    [Pg.31]    [Pg.731]    [Pg.468]    [Pg.468]    [Pg.468]    [Pg.468]    [Pg.468]    [Pg.468]    [Pg.241]    [Pg.3]    [Pg.24]    [Pg.36]    [Pg.21]    [Pg.22]    [Pg.178]   
See also in sourсe #XX -- [ Pg.326 ]

See also in sourсe #XX -- [ Pg.228 , Pg.230 ]




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