Isothermal cloud-point curves

In Figure 2.15 [66] experimental isothermal cloud-point curves of the linear low density polyethylene + hexane system are compared with the results of a fit of these data using the Sanchez-Lacombe equation of state. The pure component parameters of hexane were calculated from the critical point of hexane and its acentric factor [67]. The pure component parameters of the polymer were obtained from a simultaneous fit of PVT data and the data presented in Figure 2.15. The equations solved were those described by Koak and Heidemann [68]. The binary interaction parameter was linearly dependent on temperature. The polymer was... 

Fig. 2.1S. Isothermal cloud-point curves of LLDPE -)- n-hexane. Symbols experiments curves modified Sanchez-Lacombe fit. [66].

Fig. 2.17. Isothermal cloud-point curves of the HOPE + ethylene system. M = 43 kg mol , = 118 kg mor, Mz = 231 kg mol" . Symbols experimental data curves modeling results. Reproduced with permission from Ref 78.

Percus-Yevick (PY) 220, 222, 225 R-MMSA/R-MPY 222, 236 Cloud point curve 43 Cluster size, simulation 159 equilibrium 199 Cluster size distribution 155 Cluster, critical 163 CO2 4, 18, 19, 37, 43, 82, 83, 88, 91 Coarse-grained models 94-96 Coarse-graining procedure 22 Cohesive energy density 232, 252 Collective scattering function 13 Collision frequency 124 Colloidal suspensions, crystallization 152 Colloids 54,149, 243 hard-shere 164 weakly charged 176 Compressibility 223, 232, 243 isothermal 229... 

Interaction parameters can also be calculated from values of the expansion coefficients of polymer blends 66) using Equation-of-state theories, or from values of the isothermal compressibility of the mixture B9>. They can also be obtained from measures of volume changes on mixing. The measure of a cloud point diagram itself can in principle be used to calculate an interaction parameter though the converse is usually done in that spinodal curves are simulated using interaction parameters. This will be discussed in a later section of this review. 

The MFLG model describes the vapor/liquid critical point (v = 1), v/l equilibrium data and isotherms of pure components such as -pentane and other n-alkanes quite well (Fig. 7) while polymers also fall within the scope of the model. Since linear polyethylene and M-alkanes consist of identical repeat units it has been assumed that, in a first approximation, the parameters for n-alkane/polyethylene mixtures can be set equal to zero [55]. This assumption proved to be too simplistic since the locations predicted for spinodal curves were found to be only in qualitative agreement with the measured curves and locations of miscibility gaps. However, Fig. 8 illustrates that values for mixture parameters can be found that provide a fair description of the measured LCM behavior and its pressure dependence for the system n-alkane/linear polyethylene [56, 57]. The predictive power of the procedure is considerable, as is witnessed by Fig. 9 in which the location of cloud points in pressure-temperature-composition space for -octane/n-nonane/ linear PE mixtures is predicted remarkably well in terms of the nearby spinodals. 

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