Of mixing, equation

V/1 is the molar volume of the solvent, ns and np the molar concentrations of the solvent and the polymer, respectively, and AGm the Gibbs free energy of mixing. Equation (26) reduces in the limit of infinite dilution to the well-known Van t Hoff equation... 

There is one more aspect of the entropy of mixing (Equation 11-13) that we need to mention. Let s say we were mixing 25 blue molecules with 75 red ones (because we re talking about the number of molecules, rather than moles, we will use k instead of R in the equation). The combinatorial entropy of mixing would be (Equation 11-16) ... 

This is the desired expression relating the osmotic pressure to the free energy of mixing. Equation (6.6) for the extrapolated zero-angle scattering intensity is then written as... 

To obtain a reasonable prediction of miscibility, the values of the solubility parameters are to be measured to an accuracy better than 5j - 82 < 0.2 (J/mL). The measured values of 8j (where i = 1 or 2) far exceeds the magnitude of the critical difference of these parameters, 8j - 82 < 2 (J/mL). The calculated values of 8. are claimed to be precise within 0.8 (J/mL)i/2 [Coleman et al, 1990]. The solubility parameter approach is applicable to amorphous polymer systems. In order to adopt to highly crystalline polymers, the heat and entropy of fusion (Ah j and As p respectively) is to be dealt with in free energy of mixing equation [Van Krevelen and Hoftyzer, 1976] ... 

Here, the ideal-gas entropy of mixture is given by eq, (9i22 and includes the ideal entropy of mixing. Equations and (Q.d6) reduce the calculation of mixture properties into a two-step calculation, one for the ideal-gas contributions, and one for the residual corrections. 

This theory is based on the Gibbs free energy of mixing equation " and can be expressed as ... 

The mean molar combinatorial entropy of mixing (Equation 1.1.1-50) per mole of lattice cells n = rji + ZU2 is expressed as... 

The EOS of Sanchez and Lacombe in terms of reduced pressure, temperature, and density is a transcendental equation. In combining this equation with the free energy of mixing equation from the binary interaction model, is a numerical solution needed or can an analytical solution be obtained ... 

The ccnpatibility laetween these polymers is further confirmed by using Schneierl heat of mixing equation for two cemponent polymer blends as follows ... 

We will now set out to compute the free energies for the solid and liquid phases of an ideal isomorphous binary system and the resulting phase diagram using a very simple model. If we add the entropy of mixing (Equation 12.3) to the dhemical potentials of pure A and pure B solid and we can write the free energy of the solid as... 

The advantage of using this definition as opposed to that of Eq. 6.15 lies in the range of the index of mixing. Equation 6.15 yields values between 1/n and 00, whereas Eq. 6.17 attains values between 0 and 1. The same idea that transformed Eq. 6.15 to Eq. 6.16 can also be applied to Eq. 6.17. 

Obtain Flory s entropy of mixing. Equation 2.3, from Equations 2.A.9 through 2.A.11. 

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