Flory-Huggins equations

At equal sizes of the two components and with a small Vj, the ideal AT of Fig. 2.26 is recovered, as is indicated by Eq. (14) of Fig. 7.6. With a macromolecular component 2, i.e., a very large x and also for a small concentration v the heat of fusion of the macromolecule in Eq. (15) of Fig. 7.6 can be replaced by AH x, the heat of fusion of the macromolecule per reference volume of the low-molar-mass component 1, which is often written with Eq. (16) as AH . 

Quite analogous to the phase equilibrium of the macromolecular component 2 in Eq. (13), one can also write the Flory-Huggins expression for the small-molecule component 1 (see Fig. 2.26) to complete a eutectic phase diagram (see Fig. 2.27)  

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The symbol Xs stands for the interaction energy per solvent molecule divided by kT. Combining equations (5.7) and (5.8) gives the Flory-Huggins equation for the free energy of mixing of a polymer solution ... 

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],... 

The combination of entropy and enthalpy changes finally lead to the well-known Flory-Huggins equation [53] ... 

The Flory-Huggins equation (Eq. 10) allows one to reconstruct schematic phase diagrams to express the phase separation behavior as discussed below. 

One of the most common techniques for determining x parameters for polymer-solvent systems is the vapor pressure method.(10) In this approach, the uncrosslinked polymer is exposed to solvent vapor of known pressure, p. The polymer absorbs solvent until equilibrium is established, x is related to p and V2, the volume fraction of polymer at equilibrium, by the Flory-Huggins equation (ll)... 

Note 1 The definition and the name of the term have been modified from that which appears in ref. [5] to reflect its broader use in the context of polymer blends. In its simplest form, the %. parameter is defined according to the Flory-Huggins equation for binary mixtures... 

The polymer-solvent interaction is described by the famous Flory-Huggins equation [38]... 

Tanaka and collaborators [31] further investigated the polyacrylamide behavior. Based on the Flory-Huggins equation for osmotic pressure, they... 

The interesting features of the photo-heating phase transition are that irradiation causes the originally continuous transition to become discontinuous and the transition temperature to be lowered. These can be explained using the Flory-Huggins equation of state ... 

Linking this molecular model to observed bulk fluid PVT-composition behavior requires a calculation of the number of possible configurations (microstructures) of a mixture. There is no exact method available to solve this combinatorial problem (28). ASOG assumes the athermal (no heat of mixing) Flory-Huggins equation for this purpose (118,170,171). UNIQUAC claims to have a formula that avoids this assumption, although some aspects of athermal mixing are still present in the model. 

FIGURE I Predicted and observed DOM binding constants using the Flory-Huggins equation and methylsalicylic acid as a DOM analog. 

In Section 7.1 we discussed the thermodynamic condition for a stable mixture given in the Flory-Huggins equation (Eq. 7.1-6), where AS denotes the increase of entropy due to mixing. This equation is based on Boltzmann s principle stating that the entropy of a... 

Fig. 14 Binary phase diagram for C246H494 in octacosane. The top curve shows the equilibrium liquidus for extended-chain crystals, and the bottom line the metastable liquidus for once-folded crystals. Experimental dissolution temperatures are fitted to the Flory-Huggins equation with / = 0.15 (solid lines). Vertical dotted lines (a) and (b) indicate the concentrations at which the growth rates were determined as a function of Tc in [29]. Horizontal dotted lines indicate the temperatures at which the rates were determined in [45] as a function of concentration. G(c) at Tc = 106.3 °C, measured along line (c), is shown in Fig. 12. The shading indicates schematically the crystal growth rate (black = fast), and the dashed line the position of the growth rate minimum...

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