Phase separation spinodal

We present an improved model for the flocculation of a dispersion of hard spheres in the presence of non-adsorbing polymer. The pair potential is derived from a recent theory for interacting polymer near a flat surface, and is a function of the depletion thickness. This thickness is of the order of the radius of gyration in dilute polymer solutions but decreases when the coils in solution begin to overlap. Flocculation occurs when the osmotic attraction energy, which is a consequence of the depletion, outweighs the loss in configurational entropy of the dispersed particles. Our analysis differs from that of De Hek and Vrij with respect to the dependence of the depletion thickness on the polymer concentration (i.e., we do not consider the polymer coils to be hard spheres) and to the stability criterion used (binodal, not spinodal phase separation conditions). 

Fig. 4.7 Confocal scanning microscope image of (top) a spinodal phase separation structure Ti02 thin film, and (bottom) the cross-sectional height profile of the above picture across the solid line. Reproduced with permission from Ref. [100].

Mori R, Takahashi M, Yoko T (2005) Photoelectrochemical and photocatalytic properties of multilayered Ti02 thin films with a spinodal phase separation structure prepared by a sol-gel process. J Mater Res 20 121-127... 

In the composition range showing the nodular morphology, the increase in the PEI concentration increased the viscosity of the system and the PEI phase volume, thus reducing the rate of coalescence of the epoxy nodules in the late stage of spinodal phase separation. Smaller epoxy nodules, therefore, were formed at higher PEI concentration. 

The van der Waals scheme is the simplest scheme to describe the spinodal phase separation that has been used to describe the co-existence of a polaronic gas (low density insulating phase) and a polaronic liquid (high density metallic phase) by Emin [1], or for more complex phase separation models including magnetic interactions [2-3],... 

An example of an application to polysiloxane elastomers is the characterization of binodal and spinodal phase-separated structures occurring in model PDMS networks.310-312... 

While actual chemical events involved in nucleation and crystal growth are not known a phenomenological treatment (gives some insight. Willard Gibbs (9J considered processes of phase separation of two extreme kinds. In the first, fluctuations in concentration occur which are minute in volume but large in extent of departure from the mean (the case of binodal phase separation). In the second the volume of the fluctuation is large but the deviation from the mean for the solution is minute (responsible for spinodal phase separation). In nucleation of zeolites one is conerned only with fluctuations of the first kind. 

In the metastable state, i.e. between the binodal and the spinodal, phase separation only occurs in the presence of nuclei. Spontaneous phase separation only occurs at temperatures below the spinodal, where the solution becomes unstable. The binodal and spinodal are obtained by constructing curves of AGm vs.

various values of y (i.e. for various values of temperature) and subsequently plotting the temperature vs. the tangent points and the inflection points to obtain the binodal and spinodal, respectively (see Fig. 7.7). 

Giinther-Schade, K., Schubert, D. W., and Faupel, F., Determination of the binodal and spinodal phase separation temperature in the blend system PaMS0.5-co-(Luran)/ OMMA0.95MA0,05(Lucryl) with positron annihilation lifetime spectroscopy. Macromolecules, 35, 9074—9078 (2002). 

Various terms are u in the literature for the development of a network structure ageing, annealing and maturation. In many cases network formation is clearly time dependent. In other cases network formation seems to be instantaneous and a time dependence cannot be observed. In physical networks this may be the result of a sudden temperature decrease, resulting in a spinodal phase separation. During network formation the increase in the storage modulus may be of the order of 10 or more. It is clear that a horizontal plateau... 

On the other hand, in some cases, a phase separation mechanism, which is often proposed to explain the formation of organic gels (see Section 8.2.1.2. below), agrees better with experimental results. If the initial homogeneous solution is separated into two immiscible continuous and interconnected liquid phases, the phase separation is named spinodal phase separation or spinodal decomposition. The two phases... 

Viers, B. D. Mark, J. E., Atomic Force Microscopy Investigations of Binodal and Spinodal Phase Separated Structures in Model PDMS Elastomers. Polym. Preprints 1998, 39(1), 520-521. 

Fig. 4.24 Sketch of a gelation by arrested spinodal phase separation. A space spanning network of colloidal spheres is aggregated through depletion of non-adsorbing polymer chains...

Fig. 4. Computer simulations of spinodally phase-separated regions. (Reprinted with permission, from J. W. Cahn, J. Chem. Phys., 1965, 42, 93.)...

Phase-Separated Networks. There are two basic morphologies of phase separation which could, at least in principle, produce a network structure. Firstly, a phase separation may occur which results in a localized polymer-rich region, possibly by a nucleation and growth process. This could act as a junction zone. The growth of this rich phase may be limited by geometric constraints, such as entanglements or the copolymeric nature of the molecule. Secondly, the polymer-rich phase may not be localized but form a continuous network. This is more likely to be the case when the nucleation density is high or when spinodal phase separation occurs. 

The quantity y is experimentally determined from the work to create a unit interface. For many polymer/pol5uner interfaces, the value is in the range of 20-60 J//um (39). Although equation 1 was derived for spheres, it yields a reasonable estimation of the cylindrical diameter of spinodally phase-separated IPNs. 

Figure 4.10 Coarsening during the latter stages of spinodal phase separation (36), polystyrene-Wenc/-poly(vinyl methyl ether).

Gee RFI, Lacevic N, Fried LE (2005) Atomistic simulations of spinodal phase separation preceding poiymer crystaiiization. Nat Mater 5(l) 39-43 Gupta AM, Edwards SF (1993) Mean-field theory of phase transitions in liquid-crystalline polymers. J Chem Phys 98(2) 1588-1596... 

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