Nucleation spinodal

Fig. 11. Schematic plots of the free energy barriers for a d-dimensional system with a large range r of interaction - or a polymer mixture, respectively 1 (1 — T/Tc)2 d/2 then has to be replaced by adNd/2-i(i T/Tc)2-d/2. A) refers to the mean-field critical region, where rd(l - T/Tc) 2 d/2 > 1, B) to the non-mean-field region. In this figure, kg = l, so the gradual transition from nucleation to spinodal decomposition occurs for AF /TC 1. At AF /Tc rd (1 — T/Tc) 2-d,2,l a crossover occurs from classical nucleation (Le., compact spherical droplets) to spinodal nucleation (i.e., diffuse ramified droplets). From Binder [79]...

Spinodal nucleation 218-220 - temperature 196, 239, 250, 279 Stability threshold 117 Stabilizers 123 Stereoregularity 157 Stereospecificity, selectivity 143 Styrene 76, 128... 

If the nucleation barrier is on the order of IkpT or smaller, spinodal nucleation occurs. In this case, the concept of a single bubble being a well-defined transition state breaks down. Since the free energy of the bubble is on the order of thermal fluctuations we expect many bubbles to form simultaneously in the system, and the situation is qualitatively similar to the behavior across the spinodal. In fact, thermal fluctuations destroy the meaning of a spinodal as a sharp boundary between metastable and unstable states, and for nucleation barriers which are comparable to... 

In Fig. 13 we show the size of the critical bubble. Both at the binodal and the spinodal the size of the critical bubble diverges as expected from classical nucleation theory and Cahn-Hilliard theory, respectively. The insets show that both analytical approaches agree quantitatively with the SCF calculations in the limits x Xbin and X -> Xspin, respectively. Between binodal and spinodal the critical size has a minimum. At the minimum, the size of the critical bubble is only a few segment diameters. For the parameters used in the present calculations, the minimum corresponds to rather small nucleation barriers and is close to the regime of spinodal nucleation . For most practically relevant nucleation barriers the size of the critical bubble decreases upon increasing molar fraction. 

The unstable situation caused when a spread him begins to dewet the surface has been studied [32, 33]. IDewetting generally proceeds from hole formation or retraction of the him edge [32] and hole formation can be a nucleation process or spinodal decomposition [34]. Brochart-Wyart and de Gennes provide a nice... 

Binder K 1983 Collective diffusion, nucleation, and spinodal decomposition in polymer mixtures J. Chem. Phys. 79 6387... 

Lipson (1943, 1944), who had examined a copper-nickeMron ternary alloy. A few years ago, on an occasion in honour of Mats Hillert, Cahn (1991) mapped out in masterly fashion the history of the spinodal concept and its establishment as a widespread alternative mechanism to classical nucleation in phase transformations, specially of the solid-solid variety. An excellent, up-to-date account of the present status of the theory of spinodal decomposition and its relation to experiment and to other branches of physics is by Binder (1991). The Hillert/Cahn/Hilliard theory has also proved particularly useful to modern polymer physicists concerned with structure control in polymer blends, since that theory was first applied to these materials in 1979 (see outline by Kyu 1993). 

Thermodynamics and kinetics of phase separation of polymer mixtures have benefited greatly from theories of spinodal decomposition and of classical nucleation. In fact, the best documented tests of the theory of spinodal decomposition have been performed on polymer mixtures. 

Since the prefactor in Eq. (17) is a universal constant of order unity, the barrier AF / kaT is large only very close to the coexistence curve, i.e. for 5v / v /coex, while for larger 5v / the smallness of the barrier implies a very grad il transition from nucleation to spinodal decomposition.Conversely, for N x 1 where Eq. (16) holds the transition is very sharp since the barrier stays large right up to the spinodal for qo. 

Introduction. After we have discussed examples of uncorrelated but polydisperse particle systems we now turn to materials in which there is more structure - discrete scattering indicates correlation among the domains. In order to establish such correlation, various structure evolution mechanisms are possible. They range from a stochastic volume-filling mechanism over spinodal decomposition, nucleation-and-growth mechanisms to more complex interplays that may become palpable as experimental and evaluation technique is advancing. 

Direct evidence of nucleation during the induction period will also solve a recent argument within the field of polymer science as to whether the mechanism of the induction of polymers is related to the nucleation process or to the phase separation process (including spinodal decomposition). The latter was proposed by Imai et al. based on SAXS observation of so-called cold crystallization from the quenched glass (amorphous state) of polyethylene terephthalate) (PET) [19]. They supposed that the latter mechanism could be expanded to the usual melt crystallization, but there is no experimental support for the supposition. Our results will confirm that the nucleation mechanism is correct, in the case of melt crystallization. 

Keywords Induction period Melt and glass crystallization Nucleation and growth Optical microscopy Scattering techniques Spinodal decomposition... 

Fig. 31 Structural formation model for the initial stage of polymer crystallization [19], N G nucleation and growth of oriented domains, SD spinodal decomposition into oriented and unoriented domains, Tb, Ts, and Tx bimodal, spinodal, and crystallization temperatures, respectively I isotropic, N smectic, and C crystalline...

---