Low Molecular Weight Mixtures

The van der Waals approach is applicable to gas-liquid phase separation in a one-component system. Another type of phase separation is observed in binary mixtures. Depending on thermodynamic conditions the components may be miscible or not. A simple model describing this is based on the following molar free enthalpy approximation 

Here qa = lx l)/RT and gs = gi g l)/RT are the reduced molar free enthalpies of two pure liquid components A and B. Mixing A and B gives rise to the mixing free enthalpy described by the In-terms. Note that the mole fractions are and 

1 = 1 — x j. We had obtained this contribution earlier, cf. (3.30), for mixtures of ideal gases. Here we consider liquids. Nevertheless we still assume ideal behavior. The last term is new. It introduces an additional interaction free enthalpy proportional to the two mole fractions. The quantity x is a parameter in this theory. 

Note that temperature here enters via the assumed proportionality x /T. 

This assumption accounts for the observation that phase separation usually occurs upon lowering temperature. Nevertheless this is purely empirical and more complex descriptions of x can be found. 

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Problem 3.1 Based on the lattice model for low-molecular-weight mixtures, determine the effect of non-athermal mixing on Raoult s law. 

However, the phase separation not only gains energy, but also leads to a loss of entropy. This is because the number of possible conformations of the system is lessened. When mixed, A and B molecules had access to the whole volume. Once separated, they can only reach a part of it (compare Section 7.7). Are these losses in entropy the same for Figures 8.6 a and hi The answer is no — due to how many possible conformations can be realized in either case. Obviously, this number is many orders of magnitude greater in a low molecular weight mixture of A and B than in a polymer blend. Unattached monomers in the mixture can move independently of... 

Fig. 8.6 A cartoon illustrating phase separation in (a) a low molecular weight mixture and (6) a polymer blend. A and B components are shown with empty and shaded circles, respectively.

For low-molecular-weight mixtures, the law of corresponding states is written as y =kTf(elT,ul. ),... 

It is also possible to prepare low molecular weight mixtures of ring molecules for further reactive processing (using, for instance, anion polymerization), starting... 

It is obvious that the parameter 1 of (32) (introduced via considerations concerning the establishment of microphase equilibria with polymer-containing systems) loses its physical meaning for the low molecular weight mixtures because the segments of the components are geometrically strictly separated. This is unlike the situation with polymer solutions, where the solvent enters the polymer coil, or... 

Both in case of low-molecular-weight mixtures or polymer blends, the equilibrium phase behavior is determined by the free energy of mixing of the system, AG ... 

Fig. 83. Temperature dependence of the order parameter of polymer liquid ciystals VII (1) [6], I (2) [42], XI (3) [28] and a low>molecular-weight mixture of pentyl- and heptyloxycyano-biphenyls with addition of polymer dye VI (4) [8].

For low molecular weight mixtures, the compositions of coexisting phases can be immediately read from the temperature dependence of the demixing concentrations. Because polymer samples normally contain many unlike species differing in chain length or/and with respect to other properties like molecular architecture, this procedure is usually not permissible for polymer solutions and... 

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