Polymer solution thermodynamics binodal curve

Figure 3 illustrates the thermodynamic interplay of polymer crystallization and liquid-liquid demixing in polymer solutions. The liquid-liquid binodal curve is primarily determined by the B value. With the increase of Ep values, the liquid-liquid binodal curves shift slightly upward. On the other hand, the... 

Fig. 4 Schematic phase diagrams of a polymer solution showing LL phase separation with UCST behavior. Curve s is the spinodal, curve b is the binodal, and curve g is the glass transition temperature as a function of polymer concentration. BP indicates the Berghmans point, (a) LL phase separation is the only thermodynamic transformation of the system [17,25, 36]. (b) Curve c shows the crystallization temperature of a polymer fully miscible in a solvent as a function of concentration in the solution [17, 25], The LL phase coexistence curve (combined with vitrification) is a (classical) metastable process that lies beneath the crystallization curve c. In route 1, a polymer solution is supercooled at ALj, and the only active process is polymer crystallization. In route 2, the initially homogeneous solution is supercooled to a larger undercooling than namely AL2. Crystallization may compete either with LL phase separation when reaching point C, or LL phase separation coupled with vitrification when reaching point D. At C, crystallization may take place in the polymer-rich phase. At D, both LL phase separation and crystallization may become arrested by vitrification...

Liquid—Liquid Phase Separation, in contrast to solid-liquid phase separation, lowering temperature can induce liquid-liquid phase separation of a polymer solution with an upper critical solution temperature and when the crystallization temperature of the solvent is sufficiently lower than the phase separation temperature. In an equilibrium phase diagram of a polymer solution, the spin-odal curve divides the liquid-liquid phase separation region into two regions a thermodynamically metastable region (between the binodal and spinodal) and a thermodynamically unstable region (enclosed by the spinodal) (Fig. 11). Above the... 

Equation (4.11) can be used to calculate various thermodynamic properties of polymers, in particular, the equilibrium melting point. It can be used to calculate the mixing free energy and the binodal L-L curve, as well as the coexistence L-S curve in polymer solutions. 

In polymer solutions, liquid-liquid (L-L) demixing is another common phase transition besides crystallization. The thermodynamic boundary conditions for both of them behave as the functions of polymer concentrations and temperatures, demonstrated as phase diagrams. The schematic L-L binodal and liquid-solid (L-S) coexistence curves in polymer solutions and their interception are shown in Figure 13.2. The illustrated L-L binodal contains an upper critical solution temperature. Some other solutions also contain binodals with a lower critical solution temperature. When the L-S curve intersects with the L-L curve in the overlapping temperature windows, both curves are terminated at the intersection point, which is referred to as the monotectic triple point. 

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. 

When polymers undergo phase separation in thin films, the kinetic and thermodynamic effects are expected to be pronounced. The phase separation process can be controlled to effect desired morphologies. Under suitable conditions a film deposition process can lead to pattern replication. Demixing of polymer blends can lead to structure formation. The phase separation process can be characterized by the binodal and spinodal curves. UCST is the upper critical solution temperature, which is the temperature above which the blend constituents are completely miscible in each other in all proportions. LUST behavior is not found as often in systems other than among polymers. LUST is the lower critical solution temperature. This is the... 

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