Gibbs free energy segment-molar

There have been many attempts to describe the process of mixing and solubility of polymer molecules in thermodynamic terms. By assuming that the sizes of polymer segments are similar to those of solvent molecules, Flory and Huggins derived an expression for the partial molar Gibbs free energy of dilution that included the dimensionless Flory Higgins interaction parameter X = ZAH/RT, where Z is the lattice coordination number. It is now... 

The terms between the brackets correspond to the osmotic contribution to the Gibbs free energy (AG), and they also constitute the standard expression for AG of the Flory-Huggins theory of polymer solutions [61], where < p is the volume fraction of polymer and the ratio of the equivalent number of molecular segments of solvent to polymer (usually expressed as the ratio of molar volumes of solvent and polymer). Xap is the Flory-Huggins interaction parameter of solvent and polymer and the last term of Equation 14.1 is the interfacial free energy contribution where y is the interfacial tension, the molar volume of solvent, and r the particle radius. T is temperature in Kelvin and R is the universal gas constant. 

The fourth term on the righ hand side of Eq. (30) represents the segment-molar excess Gibbs free energy G accounting for all deviations of G from the Flory-Huggins mixture (with x = 0). Explicit expressions for G and the segment-molar activity coefficients have to be taken from theoretical considerations based on statistical thermodynamics (for examples see Sect. 3.1). 

Further treatment depends on how the distribution function WB(rB, Y ) influences the segment-molar activity coefficients f and fg and the segment-molar excess Gibbs free energy G . In the most general case, G may be a functional of WjfrB, Yb) itself, and the unknown scalar ipg and the unknown distribution function WB(rB, Yg) are coupled in complicated ways, because QB(rB, Yg) in Eq. (39) contains depending on the unknown distribution function Wg(rg, Yg). 

Segment-molar excess Gibbs free energy (Eqs. (30), (78), (150))... 

Ratzsch et al. [3] suggested the following model for the segment-molar excess Gibbs free energy of mixing (G ) in order to describe the deviation from the Flory-Huggins mixture ... 

The influence of the chemical composition in (5) can be derived using a simplified versicai of Barker s lattice theory [55], The most important consequence of (5) is the fact that the segment-molar excess Gibbs free energy of mixing and, hence, the activity coefficients depend only oti the average value (yw) of the distribution function, but not on the distribution function itself. In continuous thermod5mamics, the phase equilibrium conditions read ... 

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