Phase separation kinetic

Another important characteristic of the late stages of phase separation kinetics, for asynnnetric mixtures, is the cluster size distribution fimction of the minority phase clusters n(R,z)dR is the number of clusters of minority phase per unit volume with radii between R and + cW. Its zeroth moment gives the mean number of clusters at time r and the first moment is proportional to die mean cluster size. 

Although in principle the microscopic Hamiltonian contains the infonnation necessary to describe the phase separation kinetics, in practice the large number of degrees of freedom in the system makes it necessary to construct a reduced description. Generally, a subset of slowly varying macrovariables, such as the hydrodynamic modes, is a usefiil starting point. The equation of motion of the macrovariables can, in principle, be derived from the microscopic... 

The fiindamental problem of understanding phase separation kinetics is then posed as finding the nature of late-time solutions of detemiinistic equations such as (A3.3.57) subject to random initial conditions. 

By virtue of their simple stnicture, some properties of continuum models can be solved analytically in a mean field approxunation. The phase behaviour interfacial properties and the wetting properties have been explored. The effect of fluctuations is hrvestigated in Monte Carlo simulations as well as non-equilibrium phenomena (e.g., phase separation kinetics). Extensions of this one-order-parameter model are described in the review by Gompper and Schick [76]. A very interesting feature of tiiese models is that effective quantities of the interface—like the interfacial tension and the bending moduli—can be expressed as a fiinctional of the order parameter profiles across an interface [78]. These quantities can then be used as input for an even more coarse-grained description. 

Fraai]e J G E M 1993 Dynamic density functional theory for micro-phase separation kinetics of block copolymer melts J. Chem. Phys. 99 9202... 

The rate of phase separation after extraction in AOT-RMs is slow [167]. Keeping this in view, there is a need to study in detail the phase separation kinetics of this reverse micellar system in order to evolve means to enhance the phase separation rate. This is a very important aspect as far as industrial adaptability of RME is concerned, since the slower separation rate may become a bottleneck as in the case of ATPE. One possible approach to enhance phase separation is the application of external fields such as electric, acoustic, and microwave to reverse micellar systems. These are shown to enhance the phase separation rate in the case of ATPE [346-348]. Employing reverse micellar systems which phase separate quickly without the need for any external effort could also be a plausible solution. Some examples of such systems are DTDPA-RMs [237], sugar esters DK-F-110 RMs [239], and NaDEHP-RMs [167,243]. 

Vasanthavada, M., W. Tong, Y. Joshi, and M. S. Kislalioglu. 2005. Phase behavior of amorphous molecular dispersions II Role of hydrogen bonding in solid solubility and phase separation kinetics. Pharm Re 2 440-448. 

Miscible blends of poly(vinyl methyl ether) and polystyrene exhibit phase separation at temperatures above 100 C as a result of a lower critical solution temperature and have a well defined phase diagram ( ). This system has become a model blend for studying thermodynamics of mixing, and phase separation kinetics and resultant morphologies obtained by nucleation and growth and spinodal decomposition mechanisms. As a result of its accessible lower critical solution temperature, the PVME/PS system was selected to examine the effects of phase separation and morphology on the damping behavior of the blends and IPNs. 

Although the theoretical study of EET in polymer systems has led to considerable recent advances, we choose in the second section of this paper to take a somewhat more pragmatic approach to the study of phase separation kinetics. To do so, we temporarily set aside any consideration of the details of any particular EET model and simply rely on a fundamental relationship between the ratio of the excimer to monomer emission intensities, and the... 

In order to improve the quantitative interpretation of the earlier studies on phase separation kinetics performed in our laboratory, [9,10] a new phase diagram was determined with narrower... 

Two sets of experiments on phase separation kinetics have been performed. The first series of experiments was designed to demonstrate the feasibility of using excimer fluorescence to test Cahn s kinetic treatment of the early stages of spinodal decomposition. 

Simultaneous cloud-point and rheological measurements were performed by driving the light beam through glass plates via an optical fiber. A relatively low temperature (130 °C) was chosen to slow down the phase-separation kinetics and to precisely correlate the responses of each technique. 

SHI Shang, M., Matsuyama, H., Maki, T., Teramoto, M., and Lloyd, D.R., Effect of ciystallization and hquid-liquid phase separation on phase-separation kinetics in poly(ethylene-co-vinyl alcohol)/glycerol solution, J. Polym. Sci. Part B Polym. Phys., 41, 184, 2003. 

Y.-H. Niu, Z.-G. Wang, X.-L. Duan, W. Shao, D.-J. Wang, J. Qiu, Thermal oxidation-induced long chain branching and its effect on phase separation kinetics of a polyethylene blend. J. Appl. Polym. Sci. 119, 530-538 (2011)... 

Nesterov, A.E., Lipatov, Y.S., Horichko, V.V., Gritsenko, O.T. Filler effects on the compatibility and phase separation kinetics of poly(vinyl acetate)-poly(methyl methacrylate) mixtures. Polymer 33(3), 619-622 (1992)... 

Phase separation kinetics Spinodal decomposition Unmixing... 

VIL Villetti, M.A., Soldi, V., Rochas, C., and Borsali, R., Phase-separation kinetics and mechanism in a methylcellulose/salt aqueous solution studied by time-resolved small-angle light scattering (SALS), Macro/wo/. Chem. Phys., 212, 1063, 2011. 

Sim] Simon, J.R, Lyon, O., Phase Separation in a Fe-Cr-Co Alloy Studied by Anomalous Small Angle X-ray Scattering , Acta Metall, 37(7), 1727-1733 (1989) (Experimental, Phase Separation, Kinetics, 20)... 

A recent application of small angle X-ray scattering is for the determination of phase separation kinetics. Rundman and Hilliard (1967) noted the correspondence between the composition fluctuations corresponding to Cahn s solution to the diffusion equation and the small angle scattering intensity which results from these composition (i.e. electron density) fluctuations (Eq. 1.34). They obtain the relation,... 

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