Polymer solution thermodynamics spinodal curve

In a sense, the spinodal gives the composition and hence the supersaturation needed for homogeneous nucleation. People have tried to develop more general nucleation theories from the thermodynamics of mixtures along these lines. It is, however, difficult, if not impossible, to predict free energy curves with sufficient accuracy. When working with polymer solutions or aqueous polymer mixtures, one often has experimentally to estimate the spinodal, to find the conditions needed for spontaneous demixing. 

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... 

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... 

Heidemann et al also presented a discontinuous method to calculate spinodal curves and critical points using two different versions of the Sanchez-Lacombe equation of state and PC-SAFT. Moreover, Krenz and Heidemann applied the modified Sanchez-Lacombe equation of state to calculate the phase behaviour of polydisperse polymer blends in hydrocarbons. In this analysis the polymer samples were represented by 100 pseudo-components. Taimoori and Panayiotou developed a lattice-fluid model incorporating the classical quasi-chemical approach and applied the model in the framework of continuous thermodynamics to polydisperse polymer solutions and mixtures. The polydispersity of the polymers was expressed by the Wesslau distribution. 

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. 

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