Entropy interaction parameter

Applying similar procedure for the entropy Equation gives TSf which is similarly related to the entropy interaction parameter,... 

More fundamental treatments of polymer solubihty go back to the lattice theory developed independentiy and almost simultaneously by Flory (13) and Huggins (14) in 1942. By imagining the solvent molecules and polymer chain segments to be distributed on a lattice, they statistically evaluated the entropy of solution. The enthalpy of solution was characterized by the Flory-Huggins interaction parameter, which is related to solubihty parameters by equation 5. For high molecular weight polymers in monomeric solvents, the Flory-Huggins solubihty criterion is X A 0.5. 

The thermodynamic linear expansion factor has been related to Flory or thermodynamic interaction parameter, %, and the entropy of dilution parameter, Xs, through the Flory-Fox [10] equations. 

Recently, the Pitzer equation has been applied to model weak electrolyte systems by Beutier and Renon ( ) and Edwards, et al. (10). Beutier and Renon used a simplified Pitzer equation for the ion-ion interaction contribution, applied Debye-McAulay s electrostatic theory (Harned and Owen, (14)) for the ion-molecule interaction contribution, and adoptee) Margules type terms for molecule-molecule interactions between the same molecular solutes. Edwards, et al. applied the Pitzer equation directly, without defining any new terms, for all interactions (ion-ion, ion-molecule, and molecule-molecule) while neglecting all ternary parameters. Bromley s (1) ideas on additivity of interaction parameters of individual ions and correlation between individual ion and partial molar entropy of ions at infinite dilution were adopted in both studies. In addition, they both neglected contributions from interactions among ions of the same sign. 

In addition to the calculations of changes in the free entropy mixing, Flory introduced the interaction parameter, %, to account for the intermolecular interactions between polymer and solvent molecules, thus giving [53]... 

Disposing the Flory-Huggins modified equation, including the free entropy of mixing per total volume, AS , as a function of conversion and the enthalpy term expressed with the interaction parameter [66-68,72] ... 

Fig. 4 a Mean-field result (solid line) for the rescaled brush free energy per polymer as a function of the inverse interaction parameter 1/F- The infinite stretching resnlt is indicated by a horizontal dotted line, the broken straight line denotes the infinite stretching result with the leading correction dne to the finite end-point distribntion entropy. b Rescaled lateral pressnre within mean-field theory (solid line) compared with the asymptotic infinite-stretching result (dotted line)... 

Statistical thermodynamic mean-field theory of polymer solutions, first formulated independently by Flory, Huggins, and Staverman, in which the thermodynamic quantities of the solution are derived from a simple concept of combinatorial entropy of mixing and a reduced Gibbs-energy parameter, the X interaction parameter. 

Interaction parameter, employed in the Floiy-Huggins theory, to account for the contribution of the noncombinatorial entropy of mixing and the enthalpy of mixing to the Gibbs energy of mixing. 

Table 1. Changes in the enthalpy (Ah) and the entropy (As) parameters appearing in the polymer-solvent interaction parameter % of NIPA-water system...

This assumption is based on the fact that the polymer-solvent interaction parameter [see Eq. (8)] of the tributyrin-cellulose tributyrate system, as evaluated from melting-point depressions, is nearly zero at about 100° C [Mandelkern and Flory (160)]. It does not follow, however, that the system is athermal, for the parameter generally involves an entropy contribution. Furthermore, the heat and entropy parts of this parameter vary with the concentration in a complicated way, especially in polar systems [see, for example, Takenaka (243) Zimm (22) Kurata (154)]. Thus it is extremely hazardous to predict dilute solution properties from concentrated solution properties such as the melting-point depression, at least on a highly quantitative level as in the present problem. 

When both components of a binary mixture have high molecular weights normal for commercial polymers, the entropy of mixing is negligible in the free energy of mixing expression [48]. The nonequilibrium interaction parameter for binary compatible mixtures in the glassy state is related to the parameter for volume interaction by [49]... 

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