Polyethylene spinodal curve

Figure 20. Binodal and experimentally accessible spinodal curves for polydimetylsiloxane [M= 94,300 Mw/Mn = 2.99] + carbon dioxide (left) and polyethylene [Mw =108,000 Mw/Mn = 1.32] + n-pentane (right) systems. [Refs. 43, 44].

Figure 19. The spinodal curve calculated " using PRISM theory for a blend of polyethylene and isotactic polypropylene = A/pp = 200). The ratios A, and Aj were estimated from the group contribution tables of Small." The ordinate is a reduced temperature defined as T = kgT/e where e is the united atom, Lennard-Jones parameter for a pair of methylene sites.

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. 

FIG. 8 Comparison of MFLG calculated spinodal curves with experimental cloud points for linear polyethylene in n-hexane at indicated pressures in bar [56]. Parameter values in Table 5. Experimental data from [40]. Pressures in bar 6 ( ), 25 (A), 50 ( ). 

CPC and spinodal curve touch each other and share a common tangent as required by thermodynamics. Only for mixtures of exactly two chemical species, e.g. pure solvent plus completely homodisperse polyethylene, is the critical point situated at a common extremum of both the spinodal and binodal curve. In the case of UCST behaviour the extremum is a maximum if it is a minimum, it is called a lower critical solution temperature (LCST). In polydisperse polymer solutions, even for polymers characterized by a narrow MWD, the critical point moves appreciably away from the extremum of the CPC towards the polymer rich side of the phase diagram as is shown in Figure 1. 

Simulation studies have also been carried out on blends of chlorinated polyethylene with poly(butyl acrylate). The results are shown in Fig. 30. It was found in this case (in a similar way to the previous example) that with the value of X obtained from heat of mixing studies at 70 °C on oligomers (—94 atm) and with the value of Qjj necessary to match the spinodal to the minimum of the cloud point (—0.235 atm/K.) the resulting spinodal was very flat bottomed and lay outside the cloud point curve, an impossible situation. To match the spinodal to the cloud point curve a much smaller value of Xj2 (and correspondingly Qij) must be chosen. This discrepancy could have resulted from differences between the low molecular weight materials used for heat... 

Fig. 29. The experimental cloud point curve and simulated spinodal for a mixture of polyfmethyl methacrylate) and chlorinated polyethylene using a value of Xj2 = —30 atm and Q,j = —0.06 atm K showing that the LCST can be simulated using data which is broadly compatible with that used in simulating a UCST in the previous figure...

Fig. 30. The experimental cloud point curve (dotted line) and simulated spinodals for blends of poly(butyl acrylate) with a chlorinated polyethylene. The initial value of X,2 = —94 atm obtained from heat of mixing data, and Che adjusted Q,2 = —0.235 atm K" give a curve which is too flat-bottomed (1). By adjusting X j using an appropriate Qjj) a closer fit can be obtained X2) Xj2 = -30Qi2 = -0.076 (3) Xjj = -10 Qjj = -0.026 (4) Xi2 = -1 Qij =. 0034 ...

Fig. 31. Experimental cloud point curve (dotted line) and simulated spinodals, for blends of an ethylene-vinyl acetate copolymer with chlorinated polyethylene. The initial curve (A) using an X,j (—4.2 Jcm ) value calculated from heat of mixing data and an adjusted (—0.0108 J cm K" ) was too flat bottomed. By adjusting (and the appropriate Q,j) a closer fit could be obtained (B) Q,j = -0.00678 (C)...

There are also systems for which x increases with temperature, for example, in a form x=A - BIT. In this case the bimodal and spinodal lines open upward, visualized by rotating the top curve in Figure 5.6, 180° around the x-axis. In this case, the system will have a lower critical solution temperature (LCST) that is, the phase separation occurs when the system is heated for example, polyethylene in hexane under 5bar pressure [59]. 

Since Freeman and Rowlinson s publication [31] the amount of experimental information in the system -alkane/polyethylene has increased considerably. Papers by Nakajima et al. [34-36], Kodama and Swinton [37, 38], Koningsveld et al. [39], and Kennis et al. [40] deal with the molar mass dependence of the LCM in terms of cloud-point curves of linear polyethylene in various alkanes, ranging from w-pentane to n-tridecane, and in binary mixtures of -alkanes. Galina et al. [41] reported a spinodal and a cloud-point curve for a polyethylene sample (M = 177 kg mol in -hexane, measured with Gordon s Pulse Induced Critical Scattering technique [42, 43]. 

FIG. 10 LCM binary binodals (heavy curves), spinodals (light curves) and critical point (O) in terms of (T — Tcrit) VS. (x2 — X2, ) for 100, 50, and 1 bar (top to bottom). Calculated for w-hexane/polyethylene with the Simha-Somcynski theory [64]. Mole fraction of pol5mier X2-... 

Figure 11 Spinodal measurements by PICS for a low density polyethylene fraction in diphenyl ether. The curve ( ) was measured by Kleintjens (sample no. 5, = 70 kgmol" ). The second curve ( ) was recently measured for the same...

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