Prigogine Square-Well Cell Model

Polymer molecules are modeled as having two distinct sets of modes contributing to the partition function in the cell models. The two modes are internal and external modes. The internal modes are used to represent the internal motions of the molecules, and the intermolecular interactions are accounted for by the external modes. Prigogine and Kondepudi [12] proposed the conceptual separation of the two modes. The PVT properties of the polymer systems will be affected by the external modes. A polymer molecule is divided into r repeat units. Each repeat unit has 3 degrees of 

Two forms of the cell model (CM) are then developed harmonic oscillator approximation and square-well approximation. Both forms assnme hexagonal closed packing (HCP) lattice structure for the cell geometry. The model developed by Paul and Di Benedetto [13] assumes that the chain segments interact with a cylindrical symmetric square-well potential. The FOV model discnssed in the earlier section uses a hard-sphere type repulsive potential along with a simple cubic (SC) lattice structure. The square-well cell model by Prigogine was modified by Dee and Walsh [14]. They introduced a numerical factor to decouple the potential from the choice of lattice strncture. A universal constant for several polymers was added and the modified cell model (MCM) was a three-parameter model. The Prigogine cell EOS model can be written as follows. 

The variables used in Equation (2.40) are similar to those used in the FOV model. The HCP lattice structure leads to the 0.8909. The Lenard-Jones/612 potential is assumed. 

They noted that the potential and hard-core cell volume were coupled by the choice of cell lattice structure. In order to decouple from a specific lattice they introduced a quantitative factor that can be used to scale the hard-core cell volume in the free volume term. The factor 1 was found to be nearly constant for several polymers and falls out as 1.07. The reduced variables and characteristic parameters used in Equation (2.41) are the same as those used for the CM model. 

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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 Prigogine square-well cell model is based upon conceptual separation of internal and external modes for polymers separately accounted for in the partition... 

What is the significance of the parameters of the Prigogine square-well cell model ... 

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... 

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