Flory-Orwoll-Vrij model

To extend the Flory-Orwoll-Vrij model to mixtures, one has to use two assumptions (i) the hard-core volumes n of the segments of all components are additive and (ii) the intermolecular energy depends in a simple way on the surface areas of contact between solvent molecules and/or polymer segments. Without any derivation, the final result for the residual solvent activity in a binary polymer solution reads ... 

There has been a broad application of this group-contribution UNIFAC-fv concept to polymer solutions in the literature. Raetzsch and Glindemann recommended the use of the real free-volume relation from the Flory-Orwoll-Vrij model to account for realistic PVT-data. Problems arise for mixtures composed from chemically different components that posses the same groups, e.g., mixtures with different isomers. Kikic et al. discussed the influence of the combinatorial part on results obtained with UNIFAC-fv calculations. Gottlieb and Herskowitz gave some polemic about the special use of the Cj-parameter within UNIFAC-fv calculations. Iwai et demonstrated the possible use of... 

Flory-Orwoll-Vrij, 1964] (FOV), [Sanchez-Lacombe, 1976-8] (S-L), and [Simha-Somcynsky, 1969] (S-S). Large deviations (< 0.01 mL/g) were observed for S-G, the two following relationships were useful only at low P and over small P-ranges, whereas S-S consistently provided the best representation of data over extended ranges of T and P, with deviations < 0.003 mL/g, comparable to the experimental uncertainties. The FOV model can be expressed as ... 

Nine different equations-of-state, EOS theories are described including Flory Orwoll Vrij (FOV) Prigogine Square Well cell model, and the Sanchez Lacombe free volume theory. When the mathematical complexity of the EOS theories increases it is prudent to watch for spurious results such as negative pressure and negative volume expansivity. Although mathematically correct these have little physical meaning in polymer science. The large molecule effects are explicitly accounted for by the lattice fluid EOS theories. The current textbooks on thermodynamics discuss... 

It is not surprising that attempts have been made to derive equations of state along purely theoretical lines. This was done by Flory, Orwoll and Vrij (1964) using a lattice model, Simha and Somcynsky (1969) (hole model) and Sanchez and Lacombe (1976) (Ising fluid lattice model). These theories have a statistical-mechanical nature they all express the state parameters in a reduced dimensionless form. The reducing parameters contain the molecular characteristics of the system, but these have to be partly adapted in order to be in agreement with the experimental data. The final equations of state are accurate, but their usefulness is limited because of their mathematical complexity. 

The first successful theoretical approach of an equation of state model for polymer solutions was the Prigogine-Flory-Patterson theory. It became popular in the version by Flory, Orwoll and Vrij and is a van-der-Waals-like theory based on the corresponding-states principle. Details of its derivation can be found in numerous papers and books and need not be repeated here. The equation of state is usually expressed in reduced form and reads ... 

Whereas the models given above can be used to correlate solvent activities in polymer solutions, attempts also have been made in the literature to develop concepts to predict solvent activities. Based on the success of the UNIFAC concept for low-molecular liquid mixtures,Oishi and Prausnitz developed an analogous concept by combining the UNIFAC-model with the free-volume model of Flory, Orwoll and Vrij. The mass fraction based activity coefficient of a solvent in a polymer solution is given by ... 

On the other hand, Sauer and Dee (1994) have demonstrated that, by refining the equation of state used in the gradient theory, by using better experimental data and a different equation of state model, the Flory, Orwoll and Vrij model (the FOV model) (Flory et al. 1964), excellent agreement, at the level of better than 1%, between theory and experiment is obtained. The square gradient coefficient still has to be adjusted somewhat from the mean-field value, but it is still treated as entirely enthalpic in origin, with no temperature dependence. 

Redlich-Kwong equation of state and Soave modification Peng-Robinson equation of state Tait equation for polymer liquids Flory, Orwoll, and Vrij models Prigogine square-well cell model Sanchez-Lacombe lattice fluid theory... 

The first equation-of-state theory developed for polymers was due to Flory, Orwoll and Vrij (1964) and Eichinger and Flory (1968), the so-called FOVE model. Each of the components is characterized by p, V and T obtained from data for the pure components. Two interaction terms, denoted Xj2 and Qi2, associated with the enthalpy and entropy of the mixture, are introduced. The equation of state is ... 

Cell Model by Flory, Orwoll, and Vrij (FOV) The cell model by Flory et al. (14) has the simpler mathematical form than the Prigogine cell model ... 

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